# How do you simplify root3(16) +root3(54) ?

Jun 12, 2017

See a solution process below:

#### Explanation:

First, rewrite the expression by rewriting each radical using this rule for radicals:

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

$\sqrt[3]{16} + \sqrt[3]{54} \implies \sqrt[3]{\textcolor{red}{8} \cdot \textcolor{b l u e}{2}} + \sqrt[3]{\textcolor{red}{27} \cdot \textcolor{b l u e}{2}} \implies$

$\left(\sqrt[3]{\textcolor{red}{8}} \cdot \sqrt[3]{\textcolor{b l u e}{2}}\right) + \left(\sqrt[3]{\textcolor{red}{27}} \cdot \sqrt[3]{\textcolor{b l u e}{2}}\right) \implies$

$2 \sqrt[3]{\textcolor{b l u e}{2}} + 3 \sqrt[3]{\textcolor{b l u e}{2}}$

We can factor and combine:

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

$5 \sqrt[3]{\textcolor{b l u e}{2}}$