# How do you simplify sqrt(18a^2)*4sqrt(3a^2)?

Jun 2, 2018

See a solution process below:

#### Explanation:

First, use this rule for radicals to rewrite the expression:

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

$\sqrt{\textcolor{red}{18 {a}^{2}}} \cdot 4 \sqrt{\textcolor{b l u e}{3 {a}^{2}}} \implies$

$4 \sqrt{\textcolor{red}{18 {a}^{2}}} \cdot \sqrt{\textcolor{b l u e}{3 {a}^{2}}} \implies$

$4 \sqrt{\textcolor{red}{18 {a}^{2}} \cdot \textcolor{b l u e}{3 {a}^{2}}} \implies$

$4 \sqrt{54 {a}^{4}}$

Next, rewrite the expression as:

$4 \sqrt{\textcolor{red}{9 {a}^{4}} \cdot \textcolor{b l u e}{6}}$

Now, use this rule for radicals to complete the simplification:

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

$4 \cdot \sqrt{\textcolor{red}{9 {a}^{4}}} \cdot \sqrt{\textcolor{b l u e}{6}} \implies$

$4 \cdot 3 {a}^{2} \cdot \sqrt{6} \implies$

$12 {a}^{2} \sqrt{6}$