How do you simplify sqrt(x^2y^3z )/sqrt(xyz)?

Oct 8, 2015

$\sqrt{x {y}^{2}}$

Explanation:

Since both radicals have the same index (2), you can combine them under one radical symbol:

$\frac{\sqrt{{x}^{2} {y}^{3} z}}{\sqrt{x y z}}$
$= \sqrt{\frac{{x}^{2} {y}^{3} z}{x y z}}$

You can now cancel the denominator:

$\sqrt{\frac{{x}^{2} {y}^{3} z}{x y z}}$
$= \sqrt{\frac{{x}^{\cancel{2}} {y}^{{\cancel{3}}^{2}} \cancel{z}}{\cancel{x y z}}}$
$= \textcolor{red}{\sqrt{x {y}^{2}}}$