# How do you simplify 4sqrt(66g^2h^4)?

Aug 28, 2017

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$4 \sqrt{66 {g}^{2} {h}^{4}} \implies \sqrt{{g}^{2} {h}^{4} \cdot 66}$

Now, use this rule for radicals to simplify:

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

$4 \sqrt{\textcolor{red}{{g}^{2} {h}^{4}} \cdot \textcolor{b l u e}{66}} \implies 4 \left(\sqrt{\textcolor{red}{{g}^{2} {h}^{4}}} \cdot \sqrt{\textcolor{b l u e}{66}}\right) \implies 4 g {h}^{2} \sqrt{66}$

$66 = 2 \times 3 \times 11$ so there is no way to factor it to smaller numbers which are squared numbers.