# What is the square root of 1/169?

Mar 15, 2018

1/13

#### Explanation:

Treat a fraction like it's two separate numbers when doing work with exponents:

$\sqrt{\frac{1}{169}} = \frac{\sqrt{1}}{\sqrt{169}}$

The square root of 1 is 1, so we only need to worry about the square root of the denominator. Luckily, 169 is a perfect square of 13 $\left({13}^{2} = 169 \Leftrightarrow \sqrt{169} = 13\right)$:

$\frac{1}{\sqrt{169}} = \frac{1}{13}$