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

Pertanyaan

Tentukan hasil operasi bilangan berikut!
a. open parentheses square root of 6 plus 6 close parentheses squared
b. open parentheses 3 square root of 3 minus square root of 5 close parentheses squared
c. open parentheses 3 x square root of 2 minus 4 close parentheses squared

Pembahasan Soal:

Ingat rumus pengkuadratan suku dua bentuk aljabar yaitu

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Sehingga

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

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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.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. Febrianti

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 07 Oktober 2021

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