# What is the square root of 5/32?

Sep 17, 2015

$\sqrt{\frac{5}{32}} = \frac{\sqrt{10}}{8}$

#### Explanation:

When simplifying square roots, you try to pull out any perfect squares (which can be simplified to integers) and leave the number inside the square root as small as possible.

For this expression, these are the steps of the simplification process:
$\sqrt{\frac{5}{32}} = \frac{\sqrt{5}}{\sqrt{32}} = \frac{\sqrt{5}}{\sqrt{16 \cdot 2}} = \frac{\sqrt{5}}{\sqrt{16} \sqrt{2}} = \frac{\sqrt{5}}{4 \sqrt{2}} = \frac{\sqrt{5}}{4 \sqrt{2}} \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{5 \cdot 2}}{4 \cdot 2} = \frac{\sqrt{10}}{8}$

This is an irrational number and in decimal form $0.3952847 \ldots$