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Hasil perkalian (6​+3​)(23​−6​) adalah ....

Pertanyaan

Hasil perkalian open parentheses square root of 6 plus square root of 3 close parentheses open parentheses 2 square root of 3 minus square root of 6 close parentheses adalah ....

  1. 2 square root of 2

  2. 3 square root of 2

  3. 12 plus 2 square root of 2

  4. 12 plus 3 square root of 2

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Berdasarkan sifat distributif perkalian yaitu 

open parentheses a plus b close parentheses open parentheses c plus d close parentheses equals a b plus a d plus b c plus b d

Maka open parentheses square root of 6 plus square root of 3 close parentheses open parentheses 2 square root of 3 minus square root of 6 close parentheses diperoleh sebagai berikut.

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

Berdasarakan 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 space a not equal to 0 space text dan end text space b not equal to 0

Sehingga 

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 3 close parentheses open parentheses 2 square root of 3 minus square root of 6 close parentheses end cell equals cell 2 square root of 3 cross times square root of 6 minus square root of 6 cross times square root of 6 plus square root of 3 cross times 2 square root of 3 minus square root of 3 cross times square root of 6 end cell row blank equals cell 2 square root of 3 cross times 6 end root minus square root of 6 cross times 6 end root plus 2 square root of 3 cross times 3 end root minus square root of 3 cross times 6 end root end cell row blank equals cell 2 square root of 18 minus square root of 36 plus 2 square root of 9 minus square root of 18 end cell row blank equals cell 2 square root of 18 minus square root of 18 minus 6 plus 2 cross times 3 end cell row blank equals cell open parentheses 2 minus 1 close parentheses square root of 18 up diagonal strike negative 6 plus 6 end strike end cell row blank equals cell square root of 18 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

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

Jadi Hasil perkalian open parentheses square root of 6 plus square root of 3 close parentheses open parentheses 2 square root of 3 minus square root of 6 close parentheses adalah 3 square root of 2.

Oleh karena itu, jawaban yang benar adalah B.

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