# How do you simplify sqrt(x^6*y^6)?

Jul 23, 2015

First rewrite, as ${x}^{6} = {\left({x}^{3}\right)}^{2} \mathmr{and} {y}^{6} = {\left({y}^{3}\right)}^{2}$

#### Explanation:

=sqrt((x^3)^2*(y^3)^2)=sqrt((x^3)^2)*sqrt((y^3)^2))

$= {x}^{3} \cdot {y}^{3} = {x}^{3} {y}^{3}$

Jul 31, 2015

$\sqrt{{x}^{6} \cdot {y}^{6}} = \left\mid {x}^{3} {y}^{3} \right\mid$
$\sqrt{{x}^{6} \cdot {y}^{6}} = \sqrt{{\left(x y\right)}^{6}} = \sqrt{{\left({\left(x y\right)}^{3}\right)}^{2}} = \left\mid {\left(x y\right)}^{3} \right\mid = \left\mid {x}^{3} {y}^{3} \right\mid$
using $\sqrt{{a}^{2}} = \left\mid a \right\mid$ for all $a \in \mathbb{R}$.
Note especially that we need the absolute value to cover the case where $a < 0$, since sqrt denotes the positive square root.