# How do you simplify sqrt(128c^6)?

Apr 23, 2016

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

#### Explanation:

Note that if $x \ge 0$ then $\sqrt{x}$ denotes the non-negative square root of $x$.

So for any Real number $x$ we find:

$\sqrt{{x}^{2}} = \sqrt{{\left\mid x \right\mid}^{2}} = \left\mid x \right\mid$

If at least one of $a , b \ge 0$ then:

$\sqrt{a b} = \sqrt{a} \sqrt{b}$

So:

$\sqrt{128 {c}^{6}} = \sqrt{2 \cdot 64 {c}^{6}} = \sqrt{2 \cdot {\left(8 {\left\mid c \right\mid}^{3}\right)}^{2}} = 8 {\left\mid c \right\mid}^{3} \sqrt{2}$