How do you simplify 3sqrt12+ 4sqrt18?

Mar 8, 2018

See a solution process below:

Explanation:

First, rewrite each radical as:

$3 \sqrt{4 \cdot 3} + 4 \sqrt{9 \cdot 2}$

Next, use this rule for radicals to simplify the radicals:

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

$3 \sqrt{\textcolor{red}{4} \cdot \textcolor{b l u e}{3}} + 4 \sqrt{\textcolor{red}{9} \cdot \textcolor{b l u e}{2}} \implies$

$3 \sqrt{\textcolor{red}{4}} \sqrt{\textcolor{b l u e}{3}} + 4 \sqrt{\textcolor{red}{9}} \sqrt{\textcolor{b l u e}{2}} \implies$

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

$6 \sqrt{3} + 12 \sqrt{2}$

Or

$6 \left(\sqrt{3} + 2 \sqrt{2}\right)$