# How do you simplify sqrt 20div sqrt 15?

Jul 23, 2018

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

#### Explanation:

We have the following:

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

$20 = 4 \cdot 5$ and $15 = 3 \cdot 5$. With this in mind, we can rewrite the radicals in this way. We now have

$\frac{\sqrt{4} \sqrt{5}}{\sqrt{3} \sqrt{5}}$

Common factors in the numerator and denominator cancel, and we're left with

$\frac{\sqrt{4} \cancel{\sqrt{5}}}{\sqrt{3} \cancel{\sqrt{5}}} \implies \frac{2}{\sqrt{3}}$

The convention is to not have an irrational number in the denominator, so we can multiply this by $\frac{\sqrt{3}}{\sqrt{3}}$.

We are essentially multiplying by $1$, and we get

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

Hope this helps!