Roboguru

Tentukan hasil operasi bilangan berikut! d. 3​(26​−25​) e. (6​+8​)(6​−3​) f. (23​−6​)(8​−2​) g. (35​−6​)(35​+6​)

Pertanyaan

Tentukan hasil operasi bilangan berikut!
d. square root of 3 open parentheses 2 square root of 6 minus square root of 25 close parentheses
e. open parentheses square root of 6 plus square root of 8 close parentheses open parentheses square root of 6 minus square root of 3 close parentheses
f. open parentheses 2 square root of 3 minus square root of 6 close parentheses open parentheses square root of 8 minus square root of 2 close parentheses
g. open parentheses 3 square root of 5 minus square root of 6 close parentheses open parentheses 3 square root of 5 plus square root of 6 close parentheses

Pembahasan Soal:

Ingat sifat distributif perkalian sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell a open parentheses b plus c close parentheses end cell equals cell a b plus b c end cell row cell open parentheses a plus b close parentheses open parentheses c plus d close parentheses end cell equals cell a c plus a d plus b c plus b d end cell end table

Sehingga

d. square root of 3 open parentheses 2 square root of 6 minus square root of 25 close parentheses diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 3 open parentheses 2 square root of 6 minus square root of 25 close parentheses end cell equals cell square root of 3 cross times 2 square root of 6 minus square root of 3 cross times square root of 25 end cell row blank equals cell square root of 3 cross times 2 square root of 6 minus square root of 3 cross times 5 end cell row blank blank blank end table

Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root comma a not equal to 0 space text dan end text space b not equal to 0 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 3 open parentheses 2 square root of 6 minus square root of 25 close parentheses end cell equals cell square root of 3 cross times 2 square root of 6 minus square root of 3 cross times square root of 25 end cell row blank equals cell square root of 3 cross times 2 square root of 6 minus square root of 3 cross times 5 end cell row blank equals cell 2 square root of 3 cross times 6 end root minus 5 square root of 3 end cell row blank equals cell 2 square root of 18 minus 5 square root of 3 end cell row blank blank blank end table

Jika n-th root of a dapat difaktorkan menjadi n-th root of p cross times q end root dengan p space text atau end text space q bilangan berpangkat n maka n-th root of a dapat disederhanakan sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 3 open parentheses 2 square root of 6 minus square root of 25 close parentheses end cell equals cell 2 square root of 3 cross times 6 end root minus 5 square root of 3 end cell row blank equals cell 2 square root of 18 minus 5 square root of 3 end cell row blank equals cell 2 square root of 9 cross times 2 end root minus 5 square root of 3 end cell row blank equals cell 2 square root of 3 squared cross times 2 end root minus 5 square root of 3 end cell row blank equals cell 2 cross times 3 square root of 2 minus 5 square root of 3 end cell row blank equals cell 6 square root of 2 minus 5 square root of 3 end cell end table

Jadi hasil dari square root of 3 open parentheses 2 square root of 6 minus square root of 25 close parentheses adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 6 square root of 2 minus 5 square root of 3 end cell end table.

e. open parentheses square root of 6 plus square root of 8 close parentheses open parentheses square root of 6 minus square root of 3 close parentheses Diperoleh sebagai berikut.

begin mathsize 12px style open parentheses square root of 6 plus square root of 8 close parentheses open parentheses square root of 6 minus square root of 3 close parentheses equals square root of 6 cross times square root of 6 minus square root of 6 cross times square root of 3 plus square root of 8 cross times square root of 6 minus square root of 8 cross times square root of 3 end style

Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root maka

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 6 plus square root of 8 close parentheses open parentheses square root of 6 minus square root of 3 close parentheses end cell equals cell square root of 6 cross times square root of 6 minus square root of 6 cross times square root of 3 plus square root of 8 cross times square root of 6 minus square root of 8 cross times square root of 3 end cell row blank equals cell square root of 6 cross times 6 end root minus square root of 6 cross times 3 end root plus square root of 8 cross times 6 end root minus square root of 8 cross times 3 end root end cell row blank equals cell square root of 36 minus square root of 18 plus square root of 48 minus square root of 24 end cell end table end style

Jika n-th root of a dapat difaktorkan menjadi n-th root of p cross times q end root dengan p space text atau end text space q bilangan berpangkat n maka n-th root of a dapat disederhanakan sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 6 plus square root of 8 close parentheses open parentheses square root of 6 minus square root of 3 close parentheses end cell equals cell square root of 6 cross times 6 end root minus square root of 6 cross times 3 end root plus square root of 8 cross times 6 end root minus square root of 8 cross times 3 end root end cell row blank equals cell square root of 36 minus square root of 18 plus square root of 48 minus square root of 24 end cell row blank equals cell 6 minus square root of 9 cross times 2 end root plus square root of 16 cross times 3 end root minus square root of 4 cross times 6 end root end cell row blank equals cell 6 minus square root of 3 squared cross times 3 end root plus square root of 4 squared cross times 3 end root minus square root of 2 squared cross times 6 end root end cell row blank equals cell 6 minus 3 square root of 3 plus 4 square root of 3 minus 2 square root of 6 end cell end table

Bentuk akar dengan akar dan bilangan pokok sama dapat dikurangkan dengan menggunakan sifat distributif sebagai berikut

a n-th root of b minus c n-th root of b equals open parentheses a minus c close parentheses n-th root of b

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 6 plus square root of 8 close parentheses open parentheses square root of 6 minus square root of 3 close parentheses end cell equals cell square root of 6 cross times 6 end root minus square root of 6 cross times 3 end root plus square root of 8 cross times 6 end root minus square root of 8 cross times 3 end root end cell row blank equals cell square root of 36 minus square root of 18 plus square root of 48 minus square root of 24 end cell row blank equals cell 6 minus square root of 9 cross times 2 end root plus square root of 16 cross times 3 end root minus square root of 4 cross times 6 end root end cell row blank equals cell 6 minus square root of 3 squared cross times 3 end root plus square root of 4 squared cross times 3 end root minus square root of 2 squared cross times 6 end root end cell row blank equals cell 6 minus 3 square root of 3 plus 4 square root of 3 minus 2 square root of 6 end cell row blank equals cell 6 minus square root of 3 open parentheses 3 minus 4 close parentheses minus 2 square root of 6 end cell row blank equals cell 6 minus open parentheses negative 1 close parentheses square root of 3 minus 2 square root of 6 end cell row blank equals cell 6 plus square root of 3 minus 2 square root of 6 end cell row blank blank blank end table

Jadi hasil dari open parentheses square root of 6 plus square root of 8 close parentheses open parentheses square root of 6 minus square root of 3 close parentheses adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 6 plus square root of 3 minus 2 square root of 6 end cell row blank blank blank end table.

f. open parentheses 2 square root of 3 minus square root of 6 close parentheses open parentheses square root of 8 minus square root of 2 close parentheses diperoleh sebagai berikut.

begin mathsize 12px style open parentheses 2 square root of 3 minus square root of 6 close parentheses open parentheses square root of 8 minus square root of 2 close parentheses equals 2 square root of 3 cross times square root of 8 minus 2 square root of 3 cross times square root of 2 minus square root of 6 cross times square root of 8 plus square root of 6 cross times square root of 2 end style

Berdasarkan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root maka

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 2 square root of 3 minus square root of 6 close parentheses open parentheses square root of 8 minus square root of 2 close parentheses end cell equals cell 2 square root of 3 cross times square root of 8 minus 2 square root of 3 cross times square root of 2 minus square root of 6 cross times square root of 8 plus square root of 6 cross times square root of 2 end cell row blank equals cell 2 square root of 3 cross times 8 end root minus 2 square root of 3 cross times 2 end root minus square root of 6 cross times 8 end root plus square root of 6 cross times 2 end root end cell row blank equals cell 2 square root of 24 minus 2 square root of 6 minus square root of 48 plus square root of 12 end cell row blank blank blank end table end style

Jika n-th root of a dapat difaktorkan menjadi n-th root of p cross times q end root dengan p space text atau end text space q bilangan berpangkat n maka n-th root of a dapat disederhanakan sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 2 square root of 3 minus square root of 6 close parentheses open parentheses square root of 8 minus square root of 2 close parentheses end cell equals cell 2 square root of 3 cross times 8 end root minus 2 square root of 3 cross times 2 end root minus square root of 6 cross times 8 end root plus square root of 6 cross times 2 end root end cell row blank equals cell 2 square root of 24 minus 2 square root of 6 minus square root of 48 plus square root of 12 end cell row blank equals cell 2 square root of 4 cross times 6 end root minus 2 square root of 6 minus square root of 16 cross times 3 end root plus square root of 4 cross times 3 end root end cell row blank equals cell 2 square root of 2 squared cross times 6 end root minus 2 square root of 6 minus square root of 4 squared cross times 3 end root plus square root of 2 squared cross times 3 end root end cell row blank equals cell 2 cross times 2 square root of 6 minus 2 square root of 6 minus 4 square root of 3 plus 2 square root of 3 end cell row blank equals cell 4 square root of 6 minus 2 square root of 6 minus 4 square root of 3 plus 2 square root of 3 end cell end table

Bentuk akar dengan akar dan bilangan pokok sama dapat dikurangkan dengan menggunakan sifat distributif sebagai berikut

a n-th root of b minus c n-th root of b equals open parentheses a minus c close parentheses n-th root of b

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 2 square root of 3 minus square root of 6 close parentheses open parentheses square root of 8 minus square root of 2 close parentheses end cell equals cell 4 square root of 6 minus 2 square root of 6 minus 4 square root of 3 plus 2 square root of 3 end cell row blank equals cell open parentheses 4 minus 2 close parentheses square root of 6 minus open parentheses 4 minus 2 close parentheses square root of 3 end cell row blank equals cell 2 square root of 6 minus 2 square root of 3 end cell end table

Jadi hasil dari open parentheses 2 square root of 3 minus square root of 6 close parentheses open parentheses square root of 8 minus square root of 2 close parentheses adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 square root of 6 minus 2 square root of 3 end cell end table.

g. Ingat rumus perkalian suku dua bentuk aljabar yaitu

open parentheses a plus b close parentheses open parentheses a minus b close parentheses equals a squared minus b squared

Sehingga open parentheses 3 square root of 5 minus square root of 6 close parentheses open parentheses 3 square root of 5 plus square root of 6 close parentheses diperoleh sebagai berikut.

open parentheses 3 square root of 5 minus square root of 6 close parentheses open parentheses 3 square root of 5 plus square root of 6 close parentheses equals open parentheses 3 square root of 5 close parentheses squared minus open parentheses square root of 6 close parentheses squared

Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu n-th root of a to the power of m end root equals a to the power of m over n end exponent comma space a not equal to 0 sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 square root of 5 minus square root of 6 close parentheses open parentheses 3 square root of 5 plus square root of 6 close parentheses end cell equals cell open parentheses 3 square root of 5 close parentheses squared minus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses 3 cross times 5 to the power of 1 half end exponent close parentheses squared minus open parentheses 6 to the power of 1 half end exponent close parentheses squared end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a cross times b close parentheses to the power of m equals a to the power of m cross times b to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 square root of 5 minus square root of 6 close parentheses open parentheses 3 square root of 5 plus square root of 6 close parentheses end cell equals cell open parentheses 3 square root of 5 close parentheses squared minus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses 3 cross times 5 to the power of 1 half end exponent close parentheses squared minus open parentheses 6 to the power of 1 half end exponent close parentheses squared end cell row blank equals cell 3 squared cross times open parentheses 5 to the power of 1 half end exponent close parentheses squared minus open parentheses 6 to the power of 1 half end exponent close parentheses squared end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent dan a to the power of 1 equals a maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 square root of 5 minus square root of 6 close parentheses open parentheses 3 square root of 5 plus square root of 6 close parentheses end cell equals cell open parentheses 3 square root of 5 close parentheses squared minus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses 3 cross times 5 to the power of 1 half end exponent close parentheses squared minus open parentheses 6 to the power of 1 half end exponent close parentheses squared end cell row blank equals cell 3 squared cross times open parentheses 5 to the power of 1 half end exponent close parentheses squared minus open parentheses 6 to the power of 1 half end exponent close parentheses squared end cell row blank equals cell 9 cross times 5 to the power of 1 half cross times 2 end exponent minus 6 to the power of 1 half cross times 2 end exponent end cell row blank equals cell 9 cross times 5 to the power of 1 minus 6 to the power of 1 end cell row blank equals cell 9 cross times 5 minus 6 end cell row blank equals cell 45 minus 6 end cell row blank equals 39 end table

Jadi hasil dari open parentheses 3 square root of 5 minus square root of 6 close parentheses open parentheses 3 square root of 5 plus square root of 6 close parentheses adalah 39.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. Febrianti

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 07 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Tentukan hasil operasi bilangan berikut! a. (6​+6)2 b. (33​−5​)2 c. (3x2​−4)2

Pembahasan Soal:

Ingat rumus pengkuadratan suku dua bentuk aljabar yaitu

Error converting from MathML to accessible text.

Sehingga

a. open parentheses square root of 6 plus 6 close parentheses squared diperoleh sebagai berikut

Error converting from MathML to accessible text.

Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu n-th root of a to the power of m end root equals a to the power of m over n end exponent maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 6 plus 6 close parentheses squared end cell equals cell open parentheses square root of 6 close parentheses squared plus 12 square root of 6 plus 36 end cell row blank equals cell open parentheses 6 to the power of 1 half end exponent close parentheses squared plus 12 square root of 6 plus 36 end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent dan a to the power of 1 equals a maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 6 plus 6 close parentheses squared end cell equals cell open parentheses square root of 6 close parentheses squared plus 12 square root of 6 plus 36 end cell row blank equals cell open parentheses 6 to the power of 1 half end exponent close parentheses squared plus 12 square root of 6 plus 36 end cell row blank equals cell 6 to the power of 1 half cross times 2 end exponent plus 12 square root of 6 plus 36 end cell row blank equals cell 6 to the power of 1 plus 12 square root of 6 plus 36 end cell row blank equals cell 6 plus 12 square root of 6 plus 36 end cell row blank equals cell 42 plus 12 square root of 6 end cell end table

Jadi hasil dari open parentheses square root of 6 plus 6 close parentheses squared adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 42 plus 12 square root of 6 end cell end table.

b. open parentheses 3 square root of 3 minus square root of 5 close parentheses squared diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 square root of 3 minus square root of 5 close parentheses squared end cell equals cell open parentheses 3 square root of 3 close parentheses squared minus 2 open parentheses 3 square root of 3 close parentheses open parentheses square root of 5 close parentheses plus open parentheses square root of 5 close parentheses squared end cell row blank equals cell open parentheses 3 square root of 3 close parentheses squared minus 6 square root of 3 cross times square root of 5 plus open parentheses square root of 5 close parentheses squared end cell end table

Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 square root of 3 minus square root of 5 close parentheses squared end cell equals cell open parentheses 3 square root of 3 close parentheses squared minus 2 open parentheses 3 square root of 3 close parentheses open parentheses square root of 5 close parentheses plus open parentheses square root of 5 close parentheses squared end cell row blank equals cell open parentheses 3 square root of 3 close parentheses squared minus 6 square root of 3 cross times square root of 5 plus open parentheses square root of 5 close parentheses squared end cell row blank equals cell open parentheses 3 square root of 3 close parentheses squared minus 6 square root of 3 cross times 5 end root plus open parentheses square root of 5 close parentheses squared end cell row blank equals cell open parentheses 3 square root of 3 close parentheses squared minus 6 square root of 15 plus open parentheses square root of 5 close parentheses squared end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a cross times b close parentheses to the power of m equals a to the power of m cross times b to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 square root of 3 minus square root of 5 close parentheses squared end cell equals cell open parentheses 3 square root of 3 close parentheses squared minus 6 square root of 15 plus open parentheses square root of 5 close parentheses squared end cell row blank equals cell 3 squared cross times open parentheses square root of 3 close parentheses squared minus 6 square root of 15 plus open parentheses square root of 5 close parentheses squared end cell row blank equals cell 9 open parentheses square root of 3 close parentheses squared minus 6 square root of 15 plus open parentheses square root of 5 close parentheses squared end cell end table

Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu n-th root of a to the power of m end root equals a to the power of m over n end exponent comma space a not equal to 0 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 square root of 3 minus square root of 5 close parentheses squared end cell equals cell open parentheses 3 square root of 3 close parentheses squared minus 6 square root of 15 plus open parentheses square root of 5 close parentheses squared end cell row blank equals cell 3 squared cross times open parentheses square root of 3 close parentheses squared minus 6 square root of 15 plus open parentheses square root of 5 close parentheses squared end cell row blank equals cell 9 open parentheses square root of 3 close parentheses squared minus 6 square root of 15 plus open parentheses square root of 5 close parentheses squared end cell row blank equals cell 9 open parentheses 3 to the power of 1 half end exponent close parentheses squared minus 6 square root of 15 plus open parentheses 5 to the power of 1 half end exponent close parentheses squared end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent dan a to the power of 1 equals a maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 square root of 3 minus square root of 5 close parentheses squared end cell equals cell 9 open parentheses square root of 3 close parentheses squared minus 6 square root of 15 plus open parentheses square root of 5 close parentheses squared end cell row blank equals cell 9 open parentheses 3 to the power of 1 half end exponent close parentheses squared minus 6 square root of 15 plus open parentheses 5 to the power of 1 half end exponent close parentheses squared end cell row blank equals cell 9 cross times 3 to the power of 1 half cross times 2 end exponent minus 6 square root of 15 plus 5 to the power of 1 half cross times 2 end exponent end cell row blank equals cell 9 cross times 3 to the power of 1 minus 6 square root of 15 plus 5 to the power of 1 end cell row blank equals cell 9 cross times 3 minus 6 square root of 15 plus 5 end cell row blank equals cell 27 minus 6 square root of 15 plus 5 end cell row blank equals cell 32 minus 6 square root of 15 end cell end table

Jadi hasil dari open parentheses 3 square root of 3 minus square root of 5 close parentheses squared adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 32 minus 6 square root of 15 end cell end table.

c. open parentheses 3 x square root of 2 minus 4 close parentheses squared diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 x square root of 2 minus 4 close parentheses squared end cell equals cell open parentheses 3 x square root of 2 close parentheses squared minus 2 open parentheses 3 x square root of 2 close parentheses open parentheses 4 close parentheses plus 4 squared end cell row blank equals cell open parentheses 3 x square root of 2 close parentheses squared minus 24 x square root of 2 plus 16 end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a cross times b close parentheses to the power of m equals a to the power of m cross times b to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 x square root of 2 minus 4 close parentheses squared end cell equals cell open parentheses 3 x square root of 2 close parentheses squared minus 2 open parentheses 3 x square root of 2 close parentheses open parentheses 4 close parentheses plus 4 squared end cell row blank equals cell open parentheses 3 x square root of 2 close parentheses squared minus 24 x square root of 2 plus 16 end cell row blank equals cell 3 squared cross times x squared cross times open parentheses square root of 2 close parentheses squared minus 24 x square root of 2 plus 16 end cell row blank equals cell 9 x squared open parentheses square root of 2 close parentheses squared minus 24 x square root of 2 plus 16 end cell end table

Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu n-th root of a to the power of m end root equals a to the power of m over n end exponent comma space a not equal to 0 maka diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 x square root of 2 minus 4 close parentheses squared end cell equals cell 9 x squared open parentheses square root of 2 close parentheses squared minus 24 x square root of 2 plus 16 end cell row blank equals cell 9 x squared open parentheses 2 to the power of 1 half end exponent close parentheses squared minus 24 x square root of 2 plus 16 end cell end table

Berdasarkan sifat bilangan berpangkat yaitu open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent dan a to the power of 1 equals a maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 x square root of 2 minus 4 close parentheses squared end cell equals cell 9 x squared open parentheses square root of 2 close parentheses squared minus 24 square root of 2 x plus 16 end cell row blank equals cell 9 x squared open parentheses 2 to the power of 1 half end exponent close parentheses squared minus 24 square root of 2 x plus 16 end cell row blank equals cell 9 x squared cross times 2 to the power of 1 half cross times 2 end exponent minus 24 square root of 2 x plus 16 end cell row blank equals cell 9 x squared cross times 2 to the power of 1 minus 24 square root of 2 x plus 16 end cell row blank equals cell 9 x squared cross times 2 minus 24 square root of 2 x plus 16 end cell row blank equals cell 18 x squared minus 24 square root of 2 x plus 16 end cell end table

Jadi hasil dari open parentheses 3 x square root of 2 minus 4 close parentheses squared adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 18 x squared minus 24 square root of 2 x plus 16 end cell end table.

1

Roboguru

Sederhanakan 7​+6​1​ dan 7​−6​1​, kemudian tentukan hasil operasi berikut! a. 7​+6​1​+7​−6​1​, b. (7​+6​1​)2 dan(7​−6​1​)2, c. (7​+6​1​−7​−6​1​)2.

Pembahasan Soal:

Diketahui fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction maka bentuk sederhana dari fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction adalah dengan merasionalkan fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction dengan cara mengalikan fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction dengan akar sekawannya yaitu square root of 7 minus square root of 6 sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction end cell equals cell fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction cross times fraction numerator square root of 7 minus square root of 6 over denominator square root of 7 minus square root of 6 end fraction end cell row blank equals cell fraction numerator square root of 7 minus square root of 6 over denominator open parentheses square root of 7 plus square root of 6 close parentheses open parentheses square root of 7 minus square root of 6 close parentheses end fraction end cell row blank equals cell fraction numerator square root of 7 minus square root of 6 over denominator square root of 7 cross times square root of 7 minus square root of 7 cross times square root of 6 plus square root of 6 cross times square root of 7 minus square root of 6 cross times square root of 6 end fraction end cell end table

Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root maka diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction end cell equals cell fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction cross times fraction numerator square root of 7 minus square root of 6 over denominator square root of 7 minus square root of 6 end fraction end cell row blank equals cell fraction numerator square root of 7 minus square root of 6 over denominator open parentheses square root of 7 plus square root of 6 close parentheses open parentheses square root of 7 minus square root of 6 close parentheses end fraction end cell row blank equals cell fraction numerator square root of 7 minus square root of 6 over denominator square root of 7 cross times square root of 7 minus square root of 7 cross times square root of 6 plus square root of 6 cross times square root of 7 minus square root of 6 cross times square root of 6 end fraction end cell row blank equals cell fraction numerator square root of 7 minus square root of 6 over denominator square root of 7 cross times 7 end root minus square root of 7 cross times 6 end root plus square root of 6 cross times 7 end root minus square root of 6 cross times 6 end root end fraction end cell row blank equals cell fraction numerator square root of 7 minus square root of 6 over denominator square root of 49 minus square root of 42 plus square root of 42 minus square root of 36 end fraction end cell row blank equals cell fraction numerator square root of 7 minus square root of 6 over denominator 7 minus 6 end fraction end cell row blank equals cell fraction numerator square root of 7 minus square root of 6 over denominator 1 end fraction end cell row blank equals cell square root of 7 minus square root of 6 end cell end table

Diketahui fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction maka bentuk sederhana dari fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction adalah dengan merasionalkan fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction dengan cara mengalikan fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction dengan akar sekawannya yaitu square root of 7 plus square root of 6 sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction end cell equals cell fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction cross times fraction numerator square root of 7 plus square root of 6 over denominator square root of 7 plus square root of 6 end fraction end cell row blank equals cell fraction numerator square root of 7 plus square root of 6 over denominator open parentheses square root of 7 minus square root of 6 close parentheses open parentheses square root of 7 plus square root of 6 close parentheses end fraction end cell row blank equals cell fraction numerator square root of 7 plus square root of 6 over denominator square root of 7 cross times square root of 7 plus square root of 7 cross times square root of 6 minus square root of 6 cross times square root of 7 minus square root of 6 cross times square root of 6 end fraction end cell end table

Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root maka diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction end cell equals cell fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction cross times fraction numerator square root of 7 plus square root of 6 over denominator square root of 7 plus square root of 6 end fraction end cell row blank equals cell fraction numerator square root of 7 plus square root of 6 over denominator open parentheses square root of 7 minus square root of 6 close parentheses open parentheses square root of 7 plus square root of 6 close parentheses end fraction end cell row blank equals cell fraction numerator square root of 7 plus square root of 6 over denominator square root of 7 cross times square root of 7 plus square root of 7 cross times square root of 6 minus square root of 6 cross times square root of 7 minus square root of 6 cross times square root of 6 end fraction end cell row blank equals cell fraction numerator square root of 7 plus square root of 6 over denominator square root of 7 cross times 7 end root plus square root of 7 cross times 6 end root minus square root of 6 cross times 7 end root minus square root of 6 cross times 6 end root end fraction end cell row blank equals cell fraction numerator square root of 7 plus square root of 6 over denominator square root of 49 plus square root of 42 minus square root of 42 minus square root of 36 end fraction end cell row blank equals cell fraction numerator square root of 7 plus square root of 6 over denominator 7 minus 6 end fraction end cell row blank equals cell fraction numerator square root of 7 plus square root of 6 over denominator 1 end fraction end cell row blank equals cell square root of 7 plus square root of 6 end cell end table

Berdasarkan hitungan di atas diperoleh bahwa table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction end cell equals cell square root of 7 minus square root of 6 end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction end cell equals cell square root of 7 plus square root of 6 end cell end table sehingga

a. fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction plus fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction diperoleh sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction plus fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction end cell equals cell square root of 7 minus square root of 6 plus square root of 7 plus square root of 6 end cell row blank equals cell square root of 7 plus square root of 7 up diagonal strike negative square root of 6 plus square root of 6 end strike end cell row blank equals cell open parentheses 1 plus 1 close parentheses square root of 7 end cell row blank equals cell 2 square root of 7 end cell end table

Jadi hasil dari fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction plus fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction adalah 2 square root of 7.

b. open parentheses fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction close parentheses squared diperoleh sebagai berikut

open parentheses fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction close parentheses squared equals open parentheses square root of 7 minus square root of 6 close parentheses squared

Berdasarkan rumus pengkuadratan suku dua bentuk aljabar yaitu 

open parentheses a minus b close parentheses squared equals a squared minus 2 a b plus b squared

Sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction close parentheses squared end cell equals cell open parentheses square root of 7 minus square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared minus 2 cross times square root of 7 cross times square root of 6 plus open parentheses square root of 6 close parentheses squared end cell end table

Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction close parentheses squared end cell equals cell open parentheses square root of 7 minus square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared minus 2 cross times square root of 7 cross times square root of 6 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared minus 2 cross times square root of 7 cross times 6 end root plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared minus 2 cross times square root of 42 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared minus 2 square root of 42 plus open parentheses square root of 6 close parentheses squared end cell end table

Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu n-th root of a to the power of m end root equals a to the power of m over n end exponent comma space a not equal to 0 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction close parentheses squared end cell equals cell open parentheses square root of 7 minus square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared minus 2 cross times square root of 7 cross times square root of 6 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared minus 2 cross times square root of 7 cross times 6 end root plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared minus 2 cross times square root of 42 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared minus 2 square root of 42 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses 7 to the power of 1 half end exponent close parentheses squared minus 2 square root of 42 plus open parentheses 6 to the power of 1 half end exponent close parentheses squared end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent dan a to the power of 1 equals a maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction close parentheses squared end cell equals cell open parentheses square root of 7 minus square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared minus 2 cross times square root of 7 cross times square root of 6 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared minus 2 cross times square root of 7 cross times 6 end root plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared minus 2 cross times square root of 42 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared minus 2 square root of 42 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses 7 to the power of 1 half end exponent close parentheses squared minus 2 square root of 42 plus open parentheses 6 to the power of 1 half end exponent close parentheses squared end cell row blank equals cell 7 to the power of 1 half cross times 2 end exponent minus 2 square root of 42 plus 6 to the power of 1 half cross times 2 end exponent end cell row blank equals cell 7 to the power of 1 minus 2 square root of 42 plus 6 to the power of 1 end cell row blank equals cell 7 minus 2 square root of 42 plus 6 end cell row blank equals cell 13 minus 2 square root of 42 end cell end table

Dan open parentheses fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction close parentheses squared diperoleh sebagai berikut

open parentheses fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction close parentheses squared equals open parentheses square root of 7 plus square root of 6 close parentheses squared

Berdasarkan rumus pengkuadratan suku dua bentuk aljabar yaitu 

open parentheses a plus b close parentheses squared equals a squared plus 2 a b plus b squared

Sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction close parentheses squared end cell equals cell open parentheses square root of 7 plus square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared plus 2 cross times square root of 7 cross times square root of 6 plus open parentheses square root of 6 close parentheses squared end cell end table

Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction close parentheses squared end cell equals cell open parentheses square root of 7 plus square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared plus 2 cross times square root of 7 cross times square root of 6 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared plus 2 cross times square root of 7 cross times 6 end root plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared plus 2 cross times square root of 42 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared plus 2 square root of 42 plus open parentheses square root of 6 close parentheses squared end cell end table

Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu n-th root of a to the power of m end root equals a to the power of m over n end exponent comma space a not equal to 0 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction close parentheses squared end cell equals cell open parentheses square root of 7 plus square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared plus 2 cross times square root of 7 cross times square root of 6 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared plus 2 cross times square root of 7 cross times 6 end root plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared plus 2 cross times square root of 42 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared plus 2 square root of 42 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses 7 to the power of 1 half end exponent close parentheses squared plus 2 square root of 42 plus open parentheses 6 to the power of 1 half end exponent close parentheses squared end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent dan a to the power of 1 equals a maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction close parentheses squared end cell equals cell open parentheses square root of 7 plus square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared plus 2 cross times square root of 7 cross times square root of 6 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared plus 2 cross times square root of 7 cross times 6 end root plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared plus 2 cross times square root of 42 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses square root of 7 close parentheses squared plus 2 square root of 42 plus open parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses 7 to the power of 1 half end exponent close parentheses squared plus 2 square root of 42 plus open parentheses 6 to the power of 1 half end exponent close parentheses squared end cell row blank equals cell 7 to the power of 1 half cross times 2 end exponent plus 2 square root of 42 plus 6 to the power of 1 half cross times 2 end exponent end cell row blank equals cell 7 to the power of 1 plus 2 square root of 42 plus 6 to the power of 1 end cell row blank equals cell 7 plus 2 square root of 42 plus 6 end cell row blank equals cell 13 plus 2 square root of 42 end cell end table

Jadi hasil dari open parentheses fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction close parentheses squared equals 13 minus 2 square root of 42 dan open parentheses fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction close parentheses squared equals 13 plus 2 square root of 42.

c. open parentheses fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction minus fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction close parentheses squared diperoleh sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction minus fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction close parentheses squared end cell equals cell open parentheses square root of 7 minus square root of 6 minus open parentheses square root of 7 plus square root of 6 close parentheses close parentheses squared end cell row blank equals cell open parentheses square root of 7 minus square root of 6 minus square root of 7 minus square root of 6 close parentheses squared end cell row blank equals cell open parentheses up diagonal strike square root of 7 minus square root of 7 end strike minus square root of 6 minus square root of 6 close parentheses squared end cell row blank equals cell open parentheses negative square root of 6 minus square root of 6 close parentheses squared end cell row blank equals cell open parentheses open parentheses negative 1 minus 1 close parentheses square root of 6 close parentheses squared end cell row blank equals cell open parentheses negative 2 square root of 6 close parentheses squared end cell end table

Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu n-th root of a to the power of m end root equals a to the power of m over n end exponent comma space a not equal to 0 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction minus fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction close parentheses squared end cell equals cell open parentheses negative 2 square root of 6 close parentheses squared end cell row blank equals cell open parentheses negative 2 cross times 6 to the power of 1 half end exponent close parentheses squared end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a cross times b close parentheses to the power of m equals a to the power of m cross times b to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction minus fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction close parentheses squared end cell equals cell open parentheses negative 2 square root of 6 close parentheses squared end cell row blank equals cell open parentheses negative 2 cross times 6 to the power of 1 half end exponent close parentheses squared end cell row blank equals cell open parentheses negative 2 close parentheses squared cross times open parentheses 6 to the power of 1 half end exponent close parentheses squared end cell end table

Berdasarkan sifat bilangan berpangkat yaitu open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent dan a to the power of 1 equals a serta bilangan negatif berpangkat genap yaitu open parentheses negative a close parentheses to the power of n equals a to the power of n comma space n space text bilangan genap end text maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction minus fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction close parentheses squared end cell equals cell open parentheses negative 2 square root of 6 close parentheses squared end cell row blank equals cell open parentheses negative 2 cross times 6 to the power of 1 half end exponent close parentheses squared end cell row blank equals cell open parentheses negative 2 close parentheses squared cross times open parentheses 6 to the power of 1 half end exponent close parentheses squared end cell row blank equals cell 4 cross times 6 to the power of 1 half cross times 2 end exponent end cell row blank equals cell 4 cross times 6 to the power of 1 end cell row blank equals cell 4 cross times 6 end cell row blank equals 24 end table

Jadi hasil dari open parentheses fraction numerator 1 over denominator square root of 7 plus square root of 6 end fraction minus fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction close parentheses squared adalah 24.

0

Roboguru

Tentukan hasil operasi bilangan berikut dalam bentuk akar! d. (4a​×34a3​)3 e. (436x​÷312x​)3 f. (38b2​×3b3​)4

Pembahasan Soal:

d. Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu n-th root of a to the power of m end root equals a to the power of m over n end exponent comma a not equal to 0 maka open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed diperoleh sebagai berikut.

open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed equals open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent cross times 3 a to the power of 3 over 4 end exponent close parentheses cubed

Berdasarkan sifat bilangan berpangkat yaitu open parentheses a cross times b close parentheses to the power of m equals a to the power of m cross times b to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed end cell equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent cross times 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell row blank equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent close parentheses cubed cross times open parentheses 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed end cell equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent cross times 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell row blank equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent close parentheses cubed cross times open parentheses 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell row blank equals cell open parentheses 4 a close parentheses to the power of 1 half cross times 3 end exponent cross times open parentheses 3 a close parentheses to the power of 3 over 4 cross times 3 end exponent end cell row blank equals cell open parentheses 4 a close parentheses to the power of 3 over 2 end exponent cross times open parentheses 3 a close parentheses to the power of 9 over 4 end exponent end cell end table

Berdasarkan sifat bilangan berpangkat a to the power of m cross times a to the power of n equals a to the power of m plus n end exponent maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed end cell equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent cross times 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell row blank equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent close parentheses cubed cross times open parentheses 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell row blank equals cell open parentheses 4 a close parentheses to the power of 1 half cross times 3 end exponent cross times open parentheses 3 a close parentheses to the power of 3 over 4 cross times 3 end exponent end cell row blank equals cell open parentheses 4 a close parentheses to the power of 3 over 2 end exponent cross times open parentheses 3 a close parentheses to the power of 9 over 4 end exponent end cell row blank equals cell 4 to the power of 3 over 2 end exponent cross times a to the power of 3 over 2 end exponent cross times 3 to the power of 9 over 4 end exponent cross times a to the power of 9 over 4 end exponent end cell row blank equals cell open parentheses 2 squared close parentheses to the power of 3 over 2 end exponent cross times a to the power of 3 over 2 plus 9 over 4 end exponent cross times 3 to the power of fraction numerator 8 plus 1 over denominator 4 end fraction end exponent end cell row blank equals cell 2 to the power of 2 cross times 3 over 2 end exponent cross times a to the power of fraction numerator 3 cross times 2 plus 9 over denominator 4 end fraction end exponent cross times 3 to the power of 8 over 4 plus 1 fourth end exponent end cell row blank equals cell 2 cubed cross times a to the power of fraction numerator 6 plus 9 over denominator 4 end fraction end exponent cross times 3 to the power of 2 plus 1 fourth end exponent end cell row blank equals cell 8 cross times a to the power of 15 over 4 end exponent cross times 3 squared cross times 3 to the power of 1 fourth end exponent end cell row blank equals cell 8 cross times 9 cross times a to the power of fraction numerator 12 plus 3 over denominator 4 end fraction end exponent cross times 3 to the power of 1 fourth end exponent end cell row blank equals cell 72 cross times a to the power of 12 over 4 plus 3 over 4 end exponent cross times 3 to the power of 1 fourth end exponent end cell row blank equals cell 72 cross times a cubed cross times a to the power of 3 over 4 end exponent cross times 3 to the power of 1 fourth end exponent end cell row blank blank blank end table

Berdasarkan sifat bilangan berpangkat pecahan yaitu a to the power of m over n end exponent equals n-th root of a to the power of m end root comma space a not equal to 0 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed end cell equals cell 72 cross times a cubed cross times a to the power of 3 over 4 end exponent cross times 3 to the power of 1 fourth end exponent end cell row blank equals cell 72 cross times a cubed cross times fourth root of a cubed end root cross times fourth root of 3 to the power of 1 end root end cell row blank equals cell 72 a cubed cross times fourth root of a cubed end root cross times fourth root of 3 end cell row blank blank blank end table

Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed end cell equals cell 72 cross times a cubed cross times a to the power of 3 over 4 end exponent cross times 3 to the power of 1 fourth end exponent end cell row blank equals cell 72 cross times a cubed cross times fourth root of a cubed end root cross times fourth root of 3 to the power of 1 end root end cell row blank equals cell 72 a cubed cross times fourth root of a cubed end root cross times fourth root of 3 end cell row blank equals cell 72 a cubed cross times fourth root of a cubed cross times 3 end root end cell row blank equals cell 72 a cubed fourth root of 3 a cubed end root end cell row blank blank blank end table

Jadi hasil dari open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed dalam bentuk akar adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 72 a cubed fourth root of 3 a cubed end root end cell row blank blank blank end table.

e. Berdasarkan aturan pembagian bentuk akar dengan akar pangkat sama yaitu fraction numerator n-th root of a over denominator n-th root of b end fraction equals n-th root of a over b end root maka open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed end cell equals cell open parentheses fraction numerator 4 cube root of 6 x end root over denominator cube root of 12 x end root end fraction close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of fraction numerator 6 x over denominator 12 x end fraction end root close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of 1 half end root close parentheses cubed end cell end table

Berdasarkan sifat bilangan berpangkat yaitu open parentheses a cross times b close parentheses to the power of m equals a to the power of m cross times b to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed end cell equals cell open parentheses fraction numerator 4 cube root of 6 x end root over denominator cube root of 12 x end root end fraction close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of fraction numerator 6 x over denominator 12 x end fraction end root close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of 1 half end root close parentheses cubed end cell row blank equals cell 4 cubed cross times open parentheses cube root of 1 half end root close parentheses cubed end cell end table

Ingat bahwa n-th root of a to the power of m end root equals open parentheses n-th root of a close parentheses to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed end cell equals cell open parentheses fraction numerator 4 cube root of 6 x end root over denominator cube root of 12 x end root end fraction close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of fraction numerator 6 x over denominator 12 x end fraction end root close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of 1 half end root close parentheses cubed end cell row blank equals cell 4 cubed cross times open parentheses cube root of 1 half end root close parentheses cubed end cell row blank equals cell 64 cross times cube root of open parentheses 1 half close parentheses cubed end root end cell row blank equals cell 64 cross times 1 half end cell row blank equals 32 end table

Jadi hasil dari open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed adalah 32.

f. Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu n-th root of a to the power of m end root equals a to the power of m over n end exponent comma a not equal to 0 maka open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 diperoleh sebagai berikut.

open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 equals open parentheses open parentheses 8 b squared close parentheses to the power of 1 third end exponent cross times 3 cross times b to the power of 3 over 2 end exponent close parentheses to the power of 4

Berdasarkan sifat bilangan berpangkat yaitu open parentheses a cross times b close parentheses to the power of m equals a to the power of m cross times b to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 end cell equals cell open parentheses open parentheses 8 b squared close parentheses to the power of 1 third end exponent cross times 3 cross times b to the power of 3 over 2 end exponent close parentheses to the power of 4 end cell row blank equals cell open parentheses open parentheses 8 b squared close parentheses to the power of 1 third end exponent close parentheses to the power of 4 cross times 3 to the power of 4 cross times open parentheses b to the power of 3 over 2 end exponent close parentheses to the power of 4 end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 end cell equals cell open parentheses open parentheses 8 b squared close parentheses to the power of 1 third end exponent cross times 3 cross times b to the power of 3 over 2 end exponent close parentheses to the power of 4 end cell row blank equals cell open parentheses open parentheses 8 b squared close parentheses to the power of 1 third end exponent close parentheses to the power of 4 cross times 3 to the power of 4 cross times open parentheses b to the power of 3 over 2 end exponent close parentheses to the power of 4 end cell row blank equals cell open parentheses 8 b squared close parentheses to the power of 1 third cross times 4 end exponent cross times 81 cross times b to the power of 3 over 2 cross times 4 end exponent end cell row blank equals cell open parentheses 8 b squared close parentheses to the power of 3 over 4 end exponent cross times 81 cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 2 cross times 3 over 4 end exponent cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 3 over 2 end exponent cross times b to the power of 6 end cell end table

Berdasarkan bilangan berpangkat a to the power of m cross times a to the power of n equals a to the power of m plus n end exponent maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 end cell equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 3 over 2 end exponent cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of fraction numerator 2 plus 1 over denominator 2 end fraction end exponent cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 2 over 2 plus 1 half end exponent cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 1 cross times b to the power of 1 half end exponent cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 1 plus 6 end exponent cross times b to the power of 1 half end exponent end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 7 cross times b to the power of 1 half end exponent end cell end table

Berdasarkan sifat bilangan berpangkat pecahan yaitu a to the power of m over n end exponent equals n-th root of a to the power of m end root maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 end cell equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 7 cross times b to the power of 1 half end exponent end cell row blank equals cell 81 b to the power of 7 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of fraction numerator 1 cross times 2 over denominator 2 cross times 2 end fraction end exponent end cell row blank equals cell 81 b to the power of 7 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 2 over 4 end exponent end cell row blank equals cell 81 b to the power of 7 fourth root of 8 cubed b squared end root end cell end table

Jadi hasil dari open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 81 b to the power of 7 fourth root of 8 cubed b squared end root. end cell end table

 

0

Roboguru

Hasil dari (5​+3​)2=....

Pembahasan Soal:

Ingat pengkuadratan suku dua bentuk aljabar berikut.

open parentheses a plus b close parentheses squared equals a squared plus 2 a b plus b squared

Sehingga open parentheses square root of 5 plus square root of 3 close parentheses squared diperoleh sebagai berikut.

open parentheses square root of 5 plus square root of 3 close parentheses squared equals open parentheses square root of 5 close parentheses squared plus 2 cross times square root of 5 cross times square root of 3 plus open parentheses square root of 3 close parentheses squared

Berdasarkan perkalian bentuk akar dengan akar pangkat sama yaitu 

n-th root of a cross times n-th root of b equals n-th root of a cross times b end root comma space a not equal to 0 space text dan end text space b not equal to 0

maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 5 plus square root of 3 close parentheses squared end cell equals cell open parentheses square root of 5 close parentheses squared plus 2 cross times square root of 5 cross times square root of 3 plus open parentheses square root of 3 close parentheses squared end cell row blank equals cell open parentheses square root of 5 close parentheses squared plus 2 cross times square root of 5 cross times 3 end root plus open parentheses square root of 3 close parentheses squared end cell row blank equals cell open parentheses square root of 5 close parentheses squared plus 2 cross times square root of 15 plus open parentheses square root of 3 close parentheses squared end cell row blank equals cell open parentheses square root of 5 close parentheses squared plus 2 square root of 15 plus open parentheses square root of 3 close parentheses squared end cell end table

Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu n-th root of a to the power of m end root equals a to the power of m over n end exponent comma a not equal to 0 sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 5 plus square root of 3 close parentheses squared end cell equals cell open parentheses square root of 5 close parentheses squared plus 2 square root of 15 plus open parentheses square root of 3 close parentheses squared end cell row blank equals cell open parentheses 5 to the power of 1 half end exponent close parentheses squared plus 2 square root of 15 plus open parentheses 3 to the power of 1 half end exponent close parentheses squared end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent dan a to the power of 1 equals a maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 5 plus square root of 3 close parentheses squared end cell equals cell open parentheses square root of 5 close parentheses squared plus 2 square root of 15 plus open parentheses square root of 3 close parentheses squared end cell row blank equals cell open parentheses 5 to the power of 1 half end exponent close parentheses squared plus 2 square root of 15 plus open parentheses 3 to the power of 1 half end exponent close parentheses squared end cell row blank equals cell 5 to the power of 1 half cross times 2 end exponent plus 2 square root of 15 plus 3 to the power of 1 half cross times 2 end exponent end cell row blank equals cell 5 to the power of 1 plus 2 square root of 15 plus 3 to the power of 1 end cell row blank equals cell 5 plus 3 plus 2 square root of 15 end cell row blank equals cell 8 plus 2 square root of 15 end cell end table

Jadi Hasil dari open parentheses square root of 5 plus square root of 3 close parentheses squared adalah 8 plus 2 square root of 15.

Oleh karena itu, jawaban yang benar adalah A.

3

Roboguru

Hasil dari (4a3​−3)2=....

Pembahasan Soal:

Ingat rumus pengkuadratan suku dua bentuk aljabar yaitu