# How do you simplify sqrt15/(2sqrt20)?

May 10, 2017

Take squares out of square roots.

#### Explanation:

Original expression: $\frac{\sqrt{15}}{2 \sqrt{20}}$

Using prime factorization for the values inside the square roots:
=sqrt(3*5)/(2sqrt(2^2*5)

Take out the ${2}^{2}$ out of the square root in the denominator:
$= \frac{\sqrt{3 \cdot 5}}{4 \sqrt{5}}$

Combine the square roots into one square root:
$= \frac{1}{4} \sqrt{\frac{3 \cdot 5}{5}}$

Cancel the $5$ in the numerator and denominator of the square root:
$= \frac{\sqrt{3}}{4}$ which is our final answer.