Simplifying Radical Expression (CtP: Check the Proof)

Can you check to see if I took the proper steps to get the right answer?

Simplify:

$\displaystyle \sqrt {\frac {36x}{y^3}}$

The answer is:

$\displaystyle

\frac {6(\sqrt {xy})}{y^2}

$

My steps:

1. Simplify the numerator so it becomes:

$\displaystyle

\frac {6\sqrt {x}}{\sqrt {y^3}}

$

2. Simplify the denominator so it becomes:

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

3. It's improper to have a radical in the denominator so multiply the denominator and number by the square root of y would simplify that:

$\displaystyle \frac {6\sqrt {x(y)}}{y\sqrt {y} * (\sqrt {y})} $

Equals:

$\displaystyle \frac {6\sqrt {xy}}{y^2}$