# How do you dividesqrt125/sqrt5?

Mar 22, 2015

Three methods:

The hard way

Rationalize the denominator.

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

Two easy ways
First:
Simplify the numerator, then reduce the fraction.

$\frac{\sqrt{125}}{\sqrt{5}} = \frac{\sqrt{25 \cdot 5}}{\sqrt{5}} = \frac{5 \sqrt{5}}{\sqrt{5}} = 5$.

Second:
Write as a single square root and reduce the fraction, then simplify:

$\frac{\sqrt{125}}{\sqrt{5}} = \sqrt{\frac{125}{5}} = \sqrt{25} = 5$.