# How do you rationalize the denominator and simplify 5/(root3(4))?

Apr 19, 2017

$\frac{5}{\sqrt{4}} = \frac{5 \sqrt{2}}{2}$

#### Explanation:

Multiply the fraction by $\frac{{4}^{\frac{2}{3}}}{{4}^{\frac{2}{3}}}$:

$\frac{5}{\sqrt{4}} \textcolor{b l u e}{\times \frac{\sqrt{4}}{\sqrt{4}} \times \frac{\sqrt{4}}{\sqrt{4}}}$

$= \frac{5 \cdot {4}^{\frac{2}{3}}}{4}$

$= \frac{5 \sqrt{16}}{4}$

$= \frac{5 \sqrt{8 \cdot 2}}{4}$

$= \frac{5 \cdot 2 \cdot \sqrt{2}}{4}$

$= \frac{5 \sqrt{2}}{2}$

Apr 19, 2017

$\frac{5}{\sqrt{4}} = \frac{5 \sqrt{2}}{2}$

#### Explanation:

Given:

$\frac{5}{\sqrt{4}}$

First note that:

$\sqrt{4} = {\left({2}^{2}\right)}^{\frac{1}{3}} = {2}^{\frac{2}{3}}$

So to make the denominator rational it will be sufficient to multiply it by $\sqrt{2}$...

$\frac{5}{\sqrt{4}} = \frac{5 \sqrt{2}}{\sqrt{4} \sqrt{2}}$

$\textcolor{w h i t e}{\frac{5}{\sqrt{4}}} = \frac{5 \sqrt{2}}{\sqrt{4 \cdot 2}}$

$\textcolor{w h i t e}{\frac{5}{\sqrt{4}}} = \frac{5 \sqrt{2}}{\sqrt{{2}^{3}}}$

$\textcolor{w h i t e}{\frac{5}{\sqrt{4}}} = \frac{5 \sqrt{2}}{2}$