# How do you simplify  (18 +sqrt(567))/9?

Oct 17, 2015

$\frac{18 + \sqrt{567}}{9} = 2 + \sqrt{7}$

#### Explanation:

$\frac{18 + \sqrt{567}}{9}$

. $\textcolor{w h i t e}{\text{XXXX}} = \frac{18}{9} + \frac{\sqrt{567}}{9}$

. $\textcolor{w h i t e}{\text{XXXX}} = 2 + \frac{\sqrt{{9}^{2} \cdot 7}}{9}$

. $\textcolor{w h i t e}{\text{XXXX}} = 2 + \frac{\sqrt{{9}^{2}} \cdot \sqrt{7}}{9}$

. $\textcolor{w h i t e}{\text{XXXX}} = 2 + \sqrt{7}$