# How do you simplify sqrt(15xy)/(3sqrt(10xy^3))?

May 12, 2018

#### Explanation:

please follow the picture . I am too lazy to type in keybord :(

May 12, 2018

$\frac{\sqrt{6}}{6 y}$

#### Explanation:

Combine the two roots into one. Then simplify.

sqrt(15xy)/(3sqrt(10xy^3)) = 1/3sqrt((15cancelxy)/(10cancelxy^3)

= 1/3sqrt(3/(2y^2)

$= \frac{1}{3 y} \frac{\sqrt{3}}{\sqrt{2}} \text{ } \leftarrow$ rationalise the denominator.

$= \frac{1}{3 y} \frac{\sqrt{3}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}$

$= \frac{\sqrt{3} \times \sqrt{2}}{3 y \times 2}$

$= \frac{\sqrt{6}}{6 y}$