How do you simplify 2 sqrt216 + 4sqrt 150?

Jul 9, 2017

See a solution process below:

Explanation:

First, we can rewrite the terms within the radicals as:

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

We can use this rule of radicals to simplify the radical terms:

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

$2 \sqrt{\textcolor{red}{36} \cdot \textcolor{b l u e}{6}} + 4 \sqrt{\textcolor{red}{25} \cdot \textcolor{b l u e}{6}} \implies 2 \sqrt{\textcolor{red}{36}} \sqrt{\textcolor{b l u e}{6}} + 4 \sqrt{\textcolor{red}{25}} \sqrt{\textcolor{b l u e}{6}} \implies$

$\left(2 \cdot 6 \sqrt{6}\right) + \left(4 \cdot 5 \sqrt{6}\right) \implies 12 \sqrt{6} + 20 \sqrt{6}$

We can now combine like terms:

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

$32 \sqrt{6}$