# What is the square root of 5 divided by the square root of 15?

Sep 21, 2015

$\frac{1}{\sqrt{3}}$
or
$\frac{\sqrt{3}}{3}$ (if you like rational denominators)

#### Explanation:

$\frac{\sqrt{5}}{\sqrt{15}}$

$= \frac{\sqrt{5}}{\sqrt{3} \cdot \sqrt{5}}$

$= \frac{\cancel{\sqrt{5}}}{\sqrt{3} \cdot \cancel{\sqrt{5}}}$

$= \frac{1}{\sqrt{3}}$

To rationalize the denominator:

$= \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

$= \frac{\sqrt{3}}{3}$