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Tentukan hasil operasi bilanganberikut! a. ( 6 ​ + 6 ) 2 b. ( 3 3 ​ − 5 ​ ) 2 c. ( 3 x 2 ​ − 4 ) 2

Tentukan hasil operasi bilangan berikut!
a. 
b. 
c. 

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R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

hasil dari adalah .

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.

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Pembahasan

Ingat rumus pengkuadratan suku dua bentuk aljabar yaitu Sehingga a. diperoleh sebagai berikut Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu maka Berdasarkan sifat bilangan berpangkat dan maka Jadi hasil dari adalah . b. diperoleh sebagai berikut. Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu maka Berdasarkan sifat bilangan berpangkat maka Bentuk akar dapat diubah menjadibilangan berpangkat yaitu maka Berdasarkan sifat bilangan berpangkat dan maka Jadi hasil dari adalah . c. diperoleh sebagai berikut. Berdasarkan sifat bilangan berpangkat maka Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu maka diperoleh Berdasarkan sifat bilangan berpangkat yaitu dan maka Jadi hasil dari adalah .

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.

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