How do you simplify sqrt(128x^6)?

Jul 7, 2015

$\sqrt{128 {x}^{6}} = 8 \sqrt{2} \left\mid {x}^{3} \right\mid$

Explanation:

$\sqrt{128 {x}^{6}} = \sqrt{128} \cdot \sqrt{{x}^{6}}$

$\textcolor{w h i t e}{\text{XXXX}}$$128 = 2 \cdot 64 = 2 \cdot {8}^{2}$
$\textcolor{w h i t e}{\text{XXXX}}$$\sqrt{128} = 8 \sqrt{2}$

$\textcolor{w h i t e}{\text{XXXX}}$${x}^{6} = {\left({x}^{3}\right)}^{2}$
$\textcolor{w h i t e}{\text{XXXX}}$$\sqrt{{x}^{6}} = \left\mid {x}^{3} \right\mid$