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

Sep 22, 2015

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

#### Explanation:

Considering your problem as:

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

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

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

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