Question

What is the square root of $1/169$?

Answer 1

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 worry about the square root of the denominator.

Luckily, $169$ is a perfect square of $13({13}^2=169\iff \sqrt{169}=13)$

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