Bentuk rasional dari 4836+5 adalah ....

Pertanyaan

Bentuk rasional dari $fraction numerator 3 square root of 6 plus square root of 5 over denominator 4 square root of 8 end fraction$ adalah $....$

$fraction numerator 6 square root of 3 plus square root of 10 over denominator 16 end fraction$
$fraction numerator 6 square root of 3 plus 2 square root of 10 over denominator 16 end fraction$
$fraction numerator 7 square root of 3 plus 2 square root of 10 over denominator 32 end fraction$
$fraction numerator 12 square root of 3 plus square root of 5 over denominator 32 end fraction$

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Merasionalkan penyebut bentuk akar dapat dilakukan dengan mengalikan penyebutnya dengan akar sekawannya sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a over denominator square root of b end fraction end cell equals cell fraction numerator a over denominator square root of b end fraction cross times fraction numerator square root of b over denominator square root of b end fraction end cell row blank equals cell fraction numerator a square root of b over denominator b end fraction end cell end table$

Sehingga $fraction numerator 3 square root of 6 plus square root of 5 over denominator 4 square root of 8 end fraction$ diperoleh sebagai berikut.

Berdasarkan aturan perkalian bentuk akar dengan bilangan 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

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 square root of 6 plus square root of 5 over denominator 4 square root of 8 end fraction end cell equals cell fraction numerator 3 square root of 6 plus square root of 5 over denominator 4 square root of 8 end fraction cross times fraction numerator square root of 8 over denominator square root of 8 end fraction end cell row blank equals cell fraction numerator open parentheses 3 square root of 6 plus square root of 5 close parentheses square root of 8 over denominator 4 cross times 8 end fraction end cell row blank equals cell fraction numerator 3 square root of 6 cross times square root of 8 plus square root of 5 cross times square root of 8 over denominator 32 end fraction end cell row blank equals cell fraction numerator 3 square root of 6 cross times 8 end root plus square root of 5 cross times 8 end root over denominator 32 end fraction end cell row blank equals cell fraction numerator 3 square root of 48 plus square root of 40 over denominator 32 end fraction end cell end table$

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 maka dapat disederhanakan sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 square root of 6 plus square root of 5 over denominator 4 square root of 8 end fraction end cell equals cell fraction numerator 3 square root of 48 plus square root of 40 over denominator 32 end fraction end cell row blank equals cell fraction numerator 3 square root of 16 cross times 3 end root plus square root of 4 cross times 10 end root over denominator 32 end fraction end cell row blank equals cell fraction numerator 3 square root of 4 squared cross times 3 end root plus square root of 2 squared cross times 10 end root over denominator 32 end fraction end cell row blank equals cell fraction numerator 3 cross times 4 square root of 3 plus 2 square root of 10 over denominator 32 end fraction end cell row blank equals cell fraction numerator 12 square root of 3 plus 2 square root of 10 over denominator 32 end fraction end cell row blank equals cell fraction numerator up diagonal strike 2 open parentheses 6 square root of 3 plus square root of 10 close parentheses over denominator begin display style stack up diagonal strike 32 with 16 below end style end fraction end cell row blank equals cell fraction numerator 6 square root of 3 plus square root of 10 over denominator 16 end fraction end cell end table$

Jadi bentuk rasional dari $fraction numerator 3 square root of 6 plus square root of 5 over denominator 4 square root of 8 end fraction$ adalah $fraction numerator 6 square root of 3 plus square root of 10 over denominator 16 end fraction$ .

Oleh karena itu, jawaban yang benar adalah A.

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