Pertanyaan

Bentuk rasional dari 12 − 2 6 2 + 3 adalah....

Bentuk rasional dari $\frac{2 + 3}{12 - 2 6}$ adalah ....

$begin mathsize 14px style negative fraction numerator 3 plus 3 square root of 2 plus 2 square root of 3 plus square root of 6 over denominator 12 end fraction end style$
$begin mathsize 14px style negative fraction numerator 3 plus 3 square root of 2 plus 2 square root of 3 plus square root of 6 over denominator 6 end fraction end style$
$begin mathsize 14px style fraction numerator 3 plus 3 square root of 2 plus 2 square root of 3 plus square root of 6 over denominator 12 end fraction end style$
$begin mathsize 14px style fraction numerator 3 plus 3 square root of 2 plus 2 square root of 3 plus square root of 6 over denominator 6 end fraction end style$

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Habis dalam

Klaim

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Perhatikan bahwa Jadi, bentuk rasional dari adalah . Dengan demikian, jawaban yang tepat adalah B.

Perhatikan bahwa

$begin mathsize 11px style fraction numerator square root of 2 plus square root of 3 over denominator square root of 12 minus 2 square root of 6 end fraction equals fraction numerator square root of 2 plus square root of 3 over denominator square root of 12 minus 2 square root of 6 end fraction cross times fraction numerator square root of 12 plus 2 square root of 6 over denominator square root of 12 plus 2 square root of 6 end fraction equals fraction numerator left parenthesis square root of 2 cross times square root of 12 right parenthesis plus left parenthesis square root of 3 cross times square root of 12 right parenthesis plus left parenthesis square root of 2 cross times 2 square root of 6 right parenthesis plus left parenthesis square root of 3 cross times 2 square root of 6 right parenthesis over denominator open parentheses square root of 12 close parentheses squared minus open parentheses 2 square root of 6 close parentheses squared end fraction equals fraction numerator square root of 24 plus square root of 36 plus 2 square root of 12 plus 2 square root of 18 over denominator 12 minus 24 end fraction equals fraction numerator square root of 4 cross times 6 end root plus 6 plus 2 square root of 4 cross times 3 end root plus 2 square root of 9 cross times 2 end root over denominator negative 12 end fraction equals fraction numerator 2 square root of 6 plus 6 plus left parenthesis 2 cross times 2 square root of 3 right parenthesis plus left parenthesis 2 cross times 3 square root of 2 right parenthesis over denominator negative 12 end fraction equals fraction numerator 6 plus 6 square root of 2 plus 4 square root of 3 plus 2 square root of 6 over denominator negative 12 end fraction equals negative fraction numerator 3 plus 3 square root of 2 plus 2 square root of 3 plus square root of 6 over denominator 6 end fraction end style$

Jadi, bentuk rasional dari $begin mathsize 14px style fraction numerator square root of 2 plus square root of 3 over denominator square root of 12 minus 2 square root of 6 end fraction end style$ adalah .

Dengan demikian, jawaban yang tepat adalah B.