Pertanyaan

Bentuk rasional dari 5 − 3 3 + 2 adalah ....

Bentuk rasional dari $\frac{3 + 2}{5 - 3}$ adalah ....

$begin mathsize 14px style fraction numerator square root of 10 plus square root of 6 minus 3 square root of 5 minus 3 square root of 3 over denominator 16 end fraction end style$
$begin mathsize 14px style fraction numerator square root of 10 plus square root of 6 plus 3 square root of 5 plus 3 square root of 3 over denominator 16 end fraction end style$
$begin mathsize 14px style fraction numerator square root of 10 minus square root of 6 plus 3 square root of 5 minus 3 square root of 3 over denominator 2 end fraction end style$

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

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

Perhatikan bahwa

$begin mathsize 12px style fraction numerator 3 plus square root of 2 over denominator square root of 5 minus square root of 3 end fraction equals fraction numerator 3 plus square root of 2 over denominator square root of 5 minus square root of 3 end fraction cross times fraction numerator square root of 5 plus square root of 3 over denominator square root of 5 plus square root of 3 end fraction equals fraction numerator open parentheses 3 plus square root of 2 close parentheses open parentheses square root of 5 plus square root of 3 close parentheses over denominator open parentheses square root of 5 close parentheses squared minus open parentheses square root of 3 close parentheses squared end fraction equals fraction numerator open parentheses 3 cross times square root of 5 close parentheses plus open parentheses square root of 2 cross times square root of 5 close parentheses plus open parentheses 3 cross times square root of 3 close parentheses plus open parentheses square root of 2 cross times square root of 3 close parentheses over denominator 5 minus 3 end fraction equals fraction numerator 3 square root of 5 plus square root of 10 plus 3 square root of 3 plus square root of 6 over denominator 2 end fraction equals fraction numerator square root of 10 plus square root of 6 plus 3 square root of 5 plus 3 square root of 3 over denominator 2 end fraction end style$

Jadi, bentuk rasional dari adalah $begin mathsize 14px style fraction numerator square root of 10 plus square root of 6 plus 3 square root of 5 plus 3 square root of 3 over denominator 2 end fraction end style$ .

Dengan demikian, jawaban yang tepat adalah D.