# How do you simplify 4sqrt(52x)+sqrt(117x)-2sqrt13?

Feb 15, 2017

$= \sqrt{13} \left(8 \sqrt{x} + 3 \sqrt{x} - 2\right)$

#### Explanation:

Write each value under the root as the product of the factors, then we can compare the terms.

$4 \sqrt{52 x} + \sqrt{117 x} - 2 \sqrt{13}$

$= 4 \sqrt{4 \times 13 x} + \sqrt{9 \times 13 x} - 2 \sqrt{13}$

$= 4 \sqrt{4} \times \sqrt{13 x} + \sqrt{9} \times \sqrt{13 x} - 2 \sqrt{13}$

$= 4 \times 2 \textcolor{red}{\sqrt{13}} \sqrt{x} + 3 \textcolor{red}{\sqrt{13}} \sqrt{x} - 2 \textcolor{red}{\sqrt{13}} \text{ } \leftarrow$ common factor

$= \textcolor{red}{\sqrt{13}} \left(8 \sqrt{x} + 3 \sqrt{x} - 2\right)$