# How do you simplify sqrt1152-sqrt338?

May 24, 2018

See a solution process below:

#### Explanation:

First, rewrite the term under each radical as:

$\sqrt{576 \cdot 2} - \sqrt{169 \cdot 2}$

Next, we can use this rule for radicals to simplify each of the radicals:

$\sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}}$

$\sqrt{\textcolor{red}{576} \cdot \textcolor{b l u e}{2}} - \sqrt{\textcolor{red}{169} \cdot \textcolor{b l u e}{2}} \implies$

$\sqrt{\textcolor{red}{576}} \sqrt{\textcolor{b l u e}{2}} - \sqrt{\textcolor{red}{169}} \sqrt{\textcolor{b l u e}{2}} \implies$

$24 \sqrt{\textcolor{b l u e}{2}} - 13 \sqrt{\textcolor{b l u e}{2}}$

We can now factor out the common term giving:

$\left(24 - 13\right) \sqrt{\textcolor{b l u e}{2}} \implies$

$11 \sqrt{\textcolor{b l u e}{2}}$