What is the square root of 15 times (square root of 12 - square root of 15)?

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What is the square root of 15 times (square root of 12 - square root of 15)?

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Answer 1 · 2015-09-22T23:38:31

I simplified up to: $6 \sqrt{5} - 15$ $6sqrt(5)-15$

Explanation:

Considering your problem as:

$\sqrt{15} (\sqrt{12} - \sqrt{15}) =$ $sqrt(15)(sqrt(12)-sqrt(15))=$
we can multiply:

$= \sqrt{15} \sqrt{12} - \sqrt{15} \sqrt{15} = \sqrt{15} \sqrt{12} - 15 =$ $=sqrt(15)sqrt(12)-sqrt(15)sqrt(15)=sqrt(15)sqrt(12)-15=$

because: $\sqrt{15} \sqrt{15} = {(\sqrt{15})}^{2} = 15$ $sqrt(15)sqrt(15)=(sqrt(15))^2=15$

Then we have:
$= \sqrt{15} \sqrt{12} - 15 = \sqrt{15 \cdot 12} - 15 = \sqrt{5 \cdot 3 \cdot 4 \cdot 3} - 15 =$ $=sqrt(15)sqrt(12)-15=sqrt(15*12)-15=sqrt(5*3*4*3)-15=$
$= \sqrt{5} \sqrt{9} \sqrt{4} - 15 = 3 \cdot 2 \sqrt{5} - 15 = 6 \sqrt{5} - 15$ $=sqrt(5)sqrt(9)sqrt(4)-15=3*2sqrt(5)-15=6sqrt(5)-15$

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What is the square root of 15 times (square root of 12 - square root of 15)?

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