# How do you calculate the square root of 20 divided by the square root of 15?

Jun 13, 2018

Eliminate common factors and you will find the answer is $\frac{2}{\sqrt{3}}$

#### Explanation:

First, let's write the expression:

$\frac{\sqrt{20}}{\sqrt{15}}$

Now, we factor each number down:

$\frac{\sqrt{20}}{\sqrt{15}} = \frac{\sqrt{5} \sqrt{4}}{\sqrt{5} \sqrt{3}}$

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

We have a common factor of $\sqrt{5}$ in both the numerator and denominator, and can therefore eliminate it:

$= \frac{2 \cancel{\sqrt{5}}}{\cancel{\sqrt{5}} \sqrt{3}}$

We now have our simplified answer:

color(green)(2/sqrt(3)