# How do you simplify sqrt(3a)*sqrt(15a)?

Feb 11, 2017

$3 a \sqrt{5}$

#### Explanation:

$\sqrt{3 a} \cdot \sqrt{15 a}$

We first multiply the numbers under the square root signs keeping both and the product under the square root sign.

$\sqrt{3 a \cdot 15 a}$

$\sqrt{45 {a}^{2}}$

Now we reduce the product to factors and remove the squares, keeping the remnant under the square root sign.

$\sqrt{3 \cdot 3 \cdot 5 \cdot a \cdot a}$

Since we have two squares ($3$ and $a$) we bring them out of the square root sign and keep the remnant ($5$) under the sign.

$3 a \sqrt{5}$