# What is 13 root 3 - 4 root 48 in radical form?

Jul 18, 2017

If the question is to simplify this expression: $13 \sqrt{3} - 4 \sqrt{48}$

Then see a solution process below:

#### Explanation:

First, rewrite the radical on the right as:

$13 \sqrt{3} - 4 \sqrt{16 \cdot 3}$

Now, use this rule of radicals to simplify the term on the right:

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

$13 \sqrt{3} - 4 \sqrt{\textcolor{red}{16} \cdot \textcolor{b l u e}{3}} \implies$

$13 \sqrt{3} - 4 \sqrt{\textcolor{red}{16}} \sqrt{\textcolor{b l u e}{3}} \implies$

$13 \sqrt{3} - \left(4 \cdot 4 \sqrt{\textcolor{b l u e}{3}}\right) \implies$

$13 \sqrt{3} - 16 \sqrt{\textcolor{b l u e}{3}}$

Next, factor our the common term to simplify the constants:

$\left(13 - 16\right) \sqrt{\textcolor{b l u e}{3}} \implies$

$- 3 \sqrt{3}$