# How do you simplify 3sqrt(96k)+2sqrt180?

Jul 23, 2018

See a solution process below:

#### Explanation:

First rewrite each term as:

$3 \sqrt{16 \cdot 6 k} + 2 \sqrt{36 \cdot 5}$

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

$3 \sqrt{\textcolor{red}{16} \cdot \textcolor{b l u e}{6 k}} + 2 \sqrt{\textcolor{red}{36} \cdot \textcolor{b l u e}{5}} \implies$

$3 \sqrt{\textcolor{red}{16} \cdot \textcolor{b l u e}{6 k}} + 2 \sqrt{\textcolor{red}{36} \cdot \textcolor{b l u e}{5}} \implies$

$3 \sqrt{\textcolor{red}{16}} \sqrt{\textcolor{b l u e}{6 k}} + 2 \sqrt{\textcolor{red}{36}} \sqrt{\textcolor{b l u e}{5}} \implies$

$\left(3 \cdot 4\right) \sqrt{\textcolor{b l u e}{6 k}} + \left(2 \cdot 6\right) \sqrt{\textcolor{b l u e}{5}} \implies$

$12 \sqrt{6 k} + 12 \sqrt{5}$

Now, facture out the common term:

$\textcolor{red}{12} \sqrt{6 k} + \textcolor{red}{12} \sqrt{5} \implies$

$\textcolor{red}{12} \left(\sqrt{6 k} + \sqrt{5}\right)$