# How do you simplify root5(12)/(4root5(-4))?

Apr 15, 2017

$\frac{\sqrt[5]{12}}{4 \sqrt[5]{- 4}} = \textcolor{red}{- \frac{\sqrt[5]{3}}{4}}$

#### Explanation:

root5(12)/(4root5(-4)

$\textcolor{w h i t e}{\text{XXX}} = \frac{\sqrt[5]{3} \cdot \cancel{\sqrt[5]{4}}}{4 \cdot \sqrt[5]{- 1} \cdot \cancel{\sqrt[5]{4}}}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{\sqrt[5]{3}}{4 \cdot \left(- 1\right)}$

$\textcolor{w h i t e}{\text{XXX}} = - \frac{\sqrt[5]{3}}{4}$

Apr 15, 2017

color(red)(=-root5(3)/4 or color(red)(=-0.311432734

#### Explanation:

root5(12)/(4root5(-4)

$\therefore = \frac{\sqrt[5]{3} \cdot {\cancel{\sqrt[5]{4}}}^{\textcolor{red}{1}}}{4 \cdot {\cancel{\sqrt[5]{4}}}^{\textcolor{red}{1}} \cdot \sqrt[5]{- 1}}$

$\therefore = \frac{\sqrt[5]{3}}{4 \cdot \left(- 1\right)}$

:.color(red)(=-root5(3)/4

:.color(red)(=-0.311432734

Alternative method:

$\therefore = {12}^{\frac{1}{5}} / \left(4 \cdot {\left(- 4\right)}^{\frac{1}{5}}\right)$

$\therefore = {12}^{0.2} / \left(4 \cdot {\left(- 4\right)}^{0.2}\right)$

using the calculator:

$\therefore = \frac{1.64375183}{4 \cdot - 1.319507911}$

$\therefore = \frac{1.64375183}{- 5.278031644}$

:.color(red)(=-0.311432734