Pertanyaan

3. Bentuk sederhana dari 15 − 10 6 adalah...

3. Bentuk sederhana dari $\frac{6}{15 - 10}$ adalah... $\;$

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Jawaban terverifikasi

Jawaban

bentuk sederhananya adalah .

bentuk sederhananya adalah $fraction numerator open parentheses 3 plus square root of 6 close parentheses square root of 10 over denominator 5 end fraction$ .

Pembahasan

Perhatikan penghitungan berikut! Jadi, bentuk sederhananya adalah .

Perhatikan penghitungan berikut!

$fraction numerator square root of 6 over denominator square root of 15 minus square root of 10 end fraction equals fraction numerator square root of 6 over denominator square root of 15 minus square root of 10 end fraction cross times fraction numerator square root of 15 plus square root of 10 over denominator square root of 15 plus square root of 10 end fraction fraction numerator square root of 6 over denominator square root of 15 minus square root of 10 end fraction equals fraction numerator square root of 6 open parentheses square root of 15 plus square root of 10 close parentheses over denominator open parentheses square root of 15 close parentheses squared minus open parentheses square root of 10 close parentheses squared end fraction fraction numerator square root of 6 over denominator square root of 15 minus square root of 10 end fraction equals fraction numerator square root of 6 open parentheses square root of 15 plus square root of 10 close parentheses over denominator 15 minus 10 end fraction fraction numerator square root of 6 over denominator square root of 15 minus square root of 10 end fraction equals fraction numerator square root of 6 open parentheses square root of 15 plus square root of 10 close parentheses over denominator 5 end fraction fraction numerator square root of 6 over denominator square root of 15 minus square root of 10 end fraction equals fraction numerator square root of 90 plus square root of 60 over denominator 5 end fraction fraction numerator square root of 6 over denominator square root of 15 minus square root of 10 end fraction equals fraction numerator square root of 9 cross times 10 end root plus square root of 6 cross times 10 end root over denominator 5 end fraction fraction numerator square root of 6 over denominator square root of 15 minus square root of 10 end fraction equals fraction numerator 3 square root of 10 plus square root of 6 square root of 10 over denominator 5 end fraction fraction numerator square root of 6 over denominator square root of 15 minus square root of 10 end fraction equals fraction numerator open parentheses 3 plus square root of 6 close parentheses square root of 10 over denominator 5 end fraction$

Jadi, bentuk sederhananya adalah $fraction numerator open parentheses 3 plus square root of 6 close parentheses square root of 10 over denominator 5 end fraction$ .