Roboguru

(32​−8​)(3125​+32​)=...

Pertanyaan

begin mathsize 14px style open parentheses 3 square root of 2 minus square root of 8 close parentheses open parentheses cube root of 125 plus square root of 32 close parentheses equals... end style 

  1. begin mathsize 14px style 8 plus 5 square root of 2 end style 

  2. begin mathsize 14px style 8 plus 5 square root of 3 end style 

  3. begin mathsize 14px style 12 minus 5 square root of 2 end style 

  4. begin mathsize 14px style 12 plus 5 square root of 3 end style 

Pembahasan Video:

Pembahasan Soal:

Ubahlah bentuk akar ke dalam bentuk yang paling sederhana terlebih dahulu, kemudian operasikan dengan bilangan lainnya.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses 3 square root of 2 minus square root of 8 close parentheses open parentheses cube root of 125 plus square root of 32 close parentheses end cell equals cell open parentheses 3 square root of 2 minus 2 square root of 2 close parentheses open parentheses 5 plus 4 square root of 2 close parentheses end cell row blank equals cell open parentheses square root of 2 close parentheses open parentheses 5 plus 4 square root of 2 close parentheses end cell row blank equals cell open parentheses square root of 2 cross times 5 close parentheses plus open parentheses square root of 2 cross times 4 square root of 2 close parentheses end cell row blank equals cell 5 square root of 2 plus 8 end cell row blank equals cell 8 plus 5 square root of 2 end cell end table end style

Jadi, jawaban yang tepat adalah A.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Puspita

Terakhir diupdate 18 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Jika a adalah 23​+5​ dan b adalah 35​−3​. Berapa hasil perhitungan dari  dan  ....

Pembahasan Soal:

Gunakan konsep perkalian bentuk akar.

Diketahui a adalah 2 square root of 3 plus square root of 5 dan b adalah 3 square root of 5 minus square root of 3. Akan ditentukan hasil perhitungan dari a dan b atau a times b.

Perhatikan perhitungan berikut.

ab====(23+5)(353)23(353)+5(353)61523+3515515+9

Diperoleh hasil perhitungan dari a dan b adalah 5 square root of 15 plus 9.

Jadi, jawaban yang tepat adalah A.

1

Roboguru

Hasil dari  adalah ....

Pembahasan Soal:

Ingat bahwa undefined

Error converting from MathML to accessible text.   

Dengan demikian, hasil dari open parentheses square root of 5 plus square root of 45 close parentheses open parentheses square root of 3 minus square root of 75 close parentheses adalah negative 16 square root of 15.           

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Jika a = 5​−62​ dan b = 8​+125​, maka nilai a2−b2 adalah ....

Pembahasan Soal:

Diketahui bahwa

begin mathsize 14px style a equals square root of 5 minus 6 square root of 2 end style 

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row b equals cell square root of 8 plus square root of 125 end cell row blank equals cell square root of 4 cross times 2 end root plus square root of 25 cross times 5 end root end cell row blank equals cell 2 square root of 2 plus 5 square root of 5 end cell end table end style 

Sehingga

begin mathsize 14px style a squared minus b squaredequals open parentheses a plus b close parentheses open parentheses a minus b close parenthesesequals open parentheses open parentheses square root of 5 minus 6 square root of 2 close parentheses plus open parentheses 2 square root of 2 plus 5 square root of 5 close parentheses close parentheses open parentheses open parentheses square root of 5 minus 6 square root of 2 close parentheses minus open parentheses 2 square root of 2 plus 5 square root of 5 close parentheses close parenthesesequals open parentheses square root of 5 minus 6 square root of 2 plus 2 square root of 2 plus 5 square root of 5 close parentheses open parentheses square root of 5 minus 6 square root of 2 minus 2 square root of 2 minus 5 square root of 5 close parenthesesequals open parentheses square root of 5 plus 5 square root of 5 minus 6 square root of 2 plus 2 square root of 2 close parentheses open parentheses square root of 5 minus 5 square root of 5 minus 6 square root of 2 minus 2 square root of 2 close parenthesesequals open parentheses 6 square root of 5 minus 4 square root of 2 close parentheses open parentheses negative 4 square root of 5 minus 8 square root of 2 close parenthesesequals negative open parentheses 6 square root of 5 cross times 4 square root of 5 close parentheses plus open parentheses 4 square root of 2 cross times 4 square root of 5 close parentheses minus open parentheses 6 square root of 5 cross times 8 square root of 2 close parentheses plus open parentheses 4 square root of 2 cross times 8 square root of 2 close parenthesesequals negative open parentheses 24 cross times 5 close parentheses plus 16 square root of 10 minus 48 square root of 10 plus open parentheses 32 cross times 2 close parenthesesequals negative 120 plus 16 square root of 10 minus 48 square root of 10 plus 64equals negative 120 plus 64 plus open parentheses 16 minus 48 close parentheses square root of 10equals negative 56 minus 32 square root of 10 end style 

Dengan demikian, nilai undefined adalah undefined.

Jadi, jawaban yang tepat adalah  A.

0

Roboguru

Tentukan hasil akar berikut (42​−35​)(22​+5​).

Pembahasan Soal:

Soal ini dapat diselesaikan dengan sifat distributif sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 4 square root of 2 minus 3 square root of 5 right parenthesis left parenthesis 2 square root of 2 plus square root of 5 right parenthesis end cell equals cell 4 square root of 2 cross times 2 square root of 2 plus 4 square root of 2 cross times square root of 5 minus 3 square root of 5 cross times 2 square root of 2 minus 3 square root of 5 cross times square root of 5 end cell row blank equals cell 16 plus 4 square root of 10 minus 6 square root of 10 minus 15 end cell row blank equals cell 1 minus 2 square root of 10 end cell end table end style

Jadi, jawaban yang tepat adalah A.

0

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​)

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.

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