# How do you simplify sqrt(108x^5y^8)/sqrt(6xy^5)?

May 11, 2016

$3 {x}^{2} \sqrt{2 {y}^{3}}$

#### Explanation:

$\frac{\sqrt{108 {x}^{5} {y}^{8}}}{\sqrt{6 x {y}^{5}}} = \sqrt{\frac{108 {x}^{5} {y}^{8}}{6 x {y}^{5}}}$
=sqrt((108/6)(x^5/x)(y^8/y^5)
=sqrt((18)(x^(5-1))(y^(8-5))
=sqrt((18)(x^4)(y^3)
$= 3 {x}^{2} \sqrt{2 {y}^{3}}$

May 11, 2016

$3 {x}^{2} y \sqrt{2 y}$

#### Explanation:

Each square root can be calculated separately, or because it is a division, it can be combined into a single square root.

$\frac{\sqrt{108 {x}^{5} {y}^{8}}}{\sqrt{6 x {y}^{5}}}$ = $\sqrt{18 {x}^{4} {y}^{3}} = \sqrt{9 \times 2 {x}^{4} {y}^{2} y}$

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