# How do you simplify 8sqrt(448)?

Jan 14, 2016

$8 \sqrt{448} = 64 \sqrt{7}$

#### Explanation:

Extracting square factors (the only one we really use here is ${2}^{2} = 4$):

$448 = {2}^{2} \times 112$
$\textcolor{w h i t e}{\text{XX}} = {2}^{2} \cdot {2}^{2} \times 28$
$\textcolor{w h i t e}{\text{XX}} = {2}^{2} \cdot {2}^{2} \cdot {2}^{2} \times 7$

$\Rightarrow$
sqrt(448) = sqrt(2^2*2^2*2^2*7
$\textcolor{w h i t e}{\text{XXX}} = \left(2 \cdot 2 \cdot 2\right) \sqrt{7}$
$\textcolor{w h i t e}{\text{XXX}} = 8 \sqrt{7}$

Therefore
$8 \sqrt{448} = 8 \cdot 8 \sqrt{7}$
$\textcolor{w h i t e}{\text{XXXX}} = 64 \sqrt{7}$