# How do you divide (2sqrt108)/sqrt(180y)?

Apr 1, 2015

$\frac{2 \sqrt{3}}{\sqrt{5 y}}$ or $\frac{2 \sqrt{15 y}}{5 y}$

$\frac{2 \sqrt{108}}{\sqrt{180 y}}$

We can factor the numbers inside the square root into perfect squares:

$\frac{2 \sqrt{36 \cdot 3}}{\sqrt{36 \cdot 5 y}}$

Since the square root of $36$ is $6$:

$\frac{2 \cdot 6 \sqrt{3}}{6 \sqrt{5 y}}$

Cancel out $6$ from both the numerator and denominator:

$\frac{2 \sqrt{3}}{\sqrt{5 y}}$

It is technically "simplified" here. If you are asked to rationalize the denominator, multiply both the numerator and the denominator by $\sqrt{5 y}$:

$\left(\frac{2 \sqrt{3}}{\sqrt{5 y}}\right) \cdot \frac{\sqrt{5 y}}{\sqrt{5 y}}$

$\frac{2 \sqrt{15 y}}{5 y}$