# How do you simplify square root of 10*square root of 12?

Sep 21, 2015

$2 \sqrt{30}$

#### Explanation:

$\sqrt{10}$ and $\sqrt{12}$ have the same index 2. Because of this, you are allowed to multiply them.
$\sqrt{10} \cdot \sqrt{12}$
$= \sqrt{10 \cdot 12}$

Factor 10 and 12 so you can easily see if there are any perfect squares.
$\sqrt{10 \cdot 12}$
$= \sqrt{5 \cdot 2 \cdot 2 \cdot 2 \cdot 3}$
$= 2 \sqrt{5 \cdot 2 \cdot 3}$
$= 2 \sqrt{30}$