# How do you simplify sqrt150 + sqrt 40?

Mar 21, 2018

$5 \sqrt{6} + 2 \sqrt{10}$

#### Explanation:

$\sqrt{150} + \sqrt{40}$
$\sqrt{25 \cdot 6} + \sqrt{40}$ $\textcolor{b l u e}{\text{Find a factor of 150 that is also a perfect square}}$
$5 \sqrt{6} + \sqrt{40}$ $\textcolor{b l u e}{\text{Since 25 is a perfect square, pull out a 5}}$
$5 \sqrt{6} + \sqrt{10 \cdot 4}$ $\textcolor{b l u e}{\text{Find a factor of 40 that is also a perfect square}}$
$5 \sqrt{6} + 2 \sqrt{10}$ $\textcolor{b l u e}{\text{Since 4 is a perfect square, pull out a 2}}$

A perfect square is a number that can be pulled out of a radical by multiplying a constant together twice $\left(5 \cdot 5 = 25\right)$.

$\sqrt{6}$ and $\sqrt{10}$ can't be simplified since there are no factors of 6 or 10 that are perfect squares.