Pertanyaan

Hasil dari 12 + 108 32 − 2 6 48 + 3 adalah ....

Hasil dari $\frac{32}{12 + 108} - \frac{48 + 3}{2 6}$ adalah ....

$begin mathsize 14px style fraction numerator 12 square root of 2 minus 11 square root of 6 over denominator 12 end fraction end style$
$begin mathsize 14px style fraction numerator 12 square root of 2 minus 5 square root of 6 over denominator 12 end fraction end style$
$begin mathsize 14px style fraction numerator 6 square root of 2 minus 11 square root of 6 over denominator 6 end fraction end style$
$begin mathsize 14px style fraction numerator 6 square root of 2 minus square root of 6 over denominator 6 end fraction end style$

8 dari 10 siswa nilainya naik

dengan paket belajar pilihan

Habis dalam

Klaim

J. Joko

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Ingat kembali sifat berikut . Lalu, perhatikan perhitungan berikut! Jadi, hasil dari adalah . Dengan demikian, jawaban yang tepat adalah A.

Ingat kembali sifat berikut $\sqrt{\left({\color[rgb]{1.0, 0.0, 0.0}a}+{\color[rgb]{0.0, 0.0, 1.0}b}\right)+2\sqrt{{\color[rgb]{1.0, 0.0, 0.0}a}{\color[rgb]{0.0, 0.0, 1.0}b}}}=\sqrt{\color[rgb]{1.0, 0.0, 0.0}a}+\sqrt{\color[rgb]{0.0, 0.0, 1.0}b}$ .

Lalu, perhatikan perhitungan berikut!

$begin mathsize 12px style fraction numerator square root of 32 over denominator square root of 12 plus square root of 108 end root end fraction minus fraction numerator square root of 48 plus 3 over denominator 2 square root of 6 end fraction equals fraction numerator square root of 16 times 2 end root over denominator square root of 12 plus square root of 4 times 27 end root end root end fraction minus fraction numerator square root of 16 times 3 end root plus 3 over denominator 2 square root of 6 end fraction equals fraction numerator 4 square root of 2 over denominator square root of 12 plus 2 square root of 27 end root end fraction minus fraction numerator 4 square root of 3 plus 3 over denominator 2 square root of 6 end fraction equals fraction numerator 4 square root of 2 over denominator square root of open parentheses 9 plus 3 close parentheses plus 2 square root of 9 times 3 end root end root end fraction minus fraction numerator 4 square root of 3 plus 3 over denominator 2 square root of 6 end fraction cross times fraction numerator square root of 6 over denominator square root of 6 end fraction equals fraction numerator 4 square root of 2 over denominator square root of 9 plus square root of 3 end fraction minus fraction numerator square root of 6 open parentheses 4 square root of 3 plus 3 close parentheses over denominator 2 times 6 end fraction equals fraction numerator 4 square root of 2 over denominator 3 plus square root of 3 end fraction cross times fraction numerator 3 minus square root of 3 over denominator 3 minus square root of 3 end fraction minus fraction numerator open parentheses square root of 6 cross times 4 square root of 3 close parentheses plus open parentheses square root of 6 cross times 3 close parentheses over denominator 12 end fraction equals fraction numerator 4 square root of 2 open parentheses 3 minus square root of 3 close parentheses over denominator 3 squared minus open parentheses square root of 3 close parentheses squared end fraction minus fraction numerator 4 square root of 18 plus 3 square root of 6 over denominator 12 end fraction equals fraction numerator 4 square root of 2 open parentheses 3 minus square root of 3 close parentheses over denominator 9 minus 3 end fraction minus fraction numerator 12 square root of 2 plus 3 square root of 6 over denominator 12 end fraction equals fraction numerator 12 square root of 2 minus 4 square root of 6 over denominator 6 end fraction minus fraction numerator 12 square root of 2 plus 3 square root of 6 over denominator 12 end fraction equals fraction numerator 24 square root of 2 minus 8 square root of 6 over denominator 12 end fraction minus fraction numerator 12 square root of 2 plus 3 square root of 6 over denominator 12 end fraction equals fraction numerator 24 square root of 2 minus 8 square root of 6 minus 12 square root of 2 minus 3 square root of 6 over denominator 12 end fraction equals fraction numerator 24 square root of 2 minus 12 square root of 2 minus 8 square root of 6 minus 3 square root of 6 over denominator 12 end fraction equals fraction numerator open parentheses 24 minus 12 close parentheses square root of 2 minus open parentheses 8 plus 3 close parentheses square root of 6 over denominator 12 end fraction equals fraction numerator 12 square root of 2 minus 11 square root of 6 over denominator 12 end fraction end style$

Jadi, hasil dari adalah .

Dengan demikian, jawaban yang tepat adalah A.