How do you simplify 2 square root 216 + 4square root 150?

Mar 28, 2018

See a solution process below for:

Simplify $2 \sqrt{216} + 4 \sqrt{150}$

Explanation:

First rewrite the terms in radicals as:

$2 \sqrt{36 \cdot 6} + 4 \sqrt{25 \cdot 6}$

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

$2 \sqrt{36} \sqrt{6} + 4 \sqrt{25} \sqrt{6} \implies$

$\left(2 \cdot 6\right) \sqrt{6} + \left(4 \cdot 5\right) \sqrt{6} \implies$

$12 \sqrt{6} + 20 \sqrt{6}$

Now, we can factor our the common term to complete the simplification:

$\left(12 + 20\right) \sqrt{6} \implies$

$32 \sqrt{6}$