# How do you simplify  (64+sqrt(128) )/ 8?

Jun 27, 2015

Simplify the numerator of $\frac{64 + \sqrt{128}}{8}$ to $\frac{64 + \sqrt{2 \times 64}}{8}$. Simplify $\frac{64 + \sqrt{2 \times 64}}{8}$ to $\frac{64 + 8 \sqrt{2}}{8}$. Factor out 8 from $\frac{64 + 8 \sqrt{2}}{8}$ to get $\frac{8 \left(8 + \sqrt{2}\right)}{8}$. Cancel the $8$ in the numerator and denominator to get $8 + \sqrt{2}$.

#### Explanation:

$\frac{64 + \sqrt{128}}{8}$

Simplify.

$\frac{64 + \sqrt{2 \times 64}}{8}$ =

$\frac{64 + \sqrt{2} \sqrt{64}}{8}$ =

$\frac{64 + 8 \sqrt{2}}{8}$ =

Factor out $8$ in the numerator.

$\frac{8 \left(8 + \sqrt{2}\right)}{8}$

Cancel the $8$ in the numerator and denominator.

$\frac{\cancel{8} \left(8 + \sqrt{2}\right)}{\cancel{8}}$ =

$\left(8 + \sqrt{2}\right)$