# Question ee927

May 14, 2017

-6root(7)2+2root(7)(256)=color(red)(-2root(7)2

#### Explanation:

I have assumed $\sqrt[7]{265}$ was meant to be $\sqrt[7]{256}$

$256 = {2}^{8} = {2}^{7} \cdot 2$

$\textcolor{b l u e}{\sqrt[7]{256}} = \sqrt[7]{{2}^{7} \cdot 2} = \sqrt[7]{{2}^{7}} \cdot \sqrt[7]{2} \textcolor{b l u e}{= 2 \sqrt[7]{2}}$

-6root(7)2+2color(blue)(root(7)(256)#
$\textcolor{w h i t e}{\text{XXX}} = - 6 \sqrt[7]{2} + 2 \cdot \textcolor{b l u e}{2 \sqrt[7]{2}}$

$\textcolor{w h i t e}{\text{XXX}} = - 6 \sqrt[7]{2} + 4 \sqrt[7]{2}$

$\textcolor{w h i t e}{\text{XXX}} = - 2 \sqrt[7]{2}$