# How do you simplify root3(7/3)?

Oct 11, 2017

See a solution process below:

#### Explanation:

First, we can use this rule of radicals to rewrite expression:

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

$\sqrt[3]{\frac{\textcolor{red}{7}}{\textcolor{b l u e}{3}}} = \frac{\sqrt[3]{\textcolor{red}{7}}}{\sqrt[3]{\textcolor{b l u e}{3}}}$

To rationalize the denominator we can multiply the expression by the appropriate form of $1$:

$\frac{\sqrt[3]{9}}{\sqrt[3]{9}} \times \frac{\sqrt[3]{7}}{\sqrt[3]{3}} \implies$

$\frac{\sqrt[3]{9} \times \sqrt[3]{7}}{\sqrt[3]{9} \times \sqrt[3]{3}} \implies$

$\frac{\sqrt[3]{9 \times 7}}{\sqrt[3]{9 \times 3}} \implies$

$\frac{\sqrt[3]{63}}{\sqrt[3]{27}} \implies$

$\frac{\sqrt[3]{63}}{\sqrt[3]{{3}^{3}}} \implies$

$\frac{\sqrt[3]{63}}{3}$