# How do you multiply the square root of 5 times the square root of 125?

Sep 21, 2015

25

#### Explanation:

You can multiply them together because their radicals have the same index (2).

$\sqrt{5} \cdot \sqrt{125}$
$= \sqrt{5 \cdot 125}$
$= \sqrt{625}$
$= 25$

OR

You can try writing 125 as ${5}^{3}$ instead.

$\sqrt{5} \cdot \sqrt{125}$
$= \sqrt{5} \cdot \sqrt{{5}^{3}}$
$= \sqrt{5 \cdot {5}^{3}}$
$= \sqrt{{5}^{4}}$
$= {5}^{2}$
$= 25$