How do you simplify $\frac{\sqrt{x^{2} y^{3} z}}{\sqrt{x y z}}$ $sqrt(x^2y^3z )/sqrt(xyz)$ ?

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Answer 1 · 2015-10-08T13:48:38

$\sqrt{x y^{2}}$ $sqrt(xy^2)$

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

$\frac{\sqrt{x^{2} y^{3} z}}{\sqrt{x y z}}$ $sqrt(x^2y^3z)/sqrt(xyz)$
$= \sqrt{\frac{x^{2} y^{3} z}{x y z}}$ $=sqrt[(x^2y^3z)/(xyz)]$

You can now cancel the denominator:

$\sqrt{\frac{x^{2} y^{3} z}{x y z}}$ $sqrt[(x^2y^3z)/(xyz)]$
$=sqrt[(x^cancel2y^(cancel3^2)cancelz)/cancel(xyz)]$
$=color(red)(sqrt(xy^2))$

How do you simplify sqrt(x^2y^3z )/sqrt(xyz)√x2y3z√xyzsqrt(x^2y^3z )/sqrt(xyz)?