Incorrect. Write the radical as the quotient of two radicals and then rationalize the denominator.

$\displaystyle\sqrt{{\frac{{{45}{x}}}{{{5}{y}}}}}=\frac{\sqrt{{{45}{x}}}}{\sqrt{{{5}{y}}}}\cdot\frac{\sqrt{{{5}{y}}}}{\sqrt{{{5}{y}}}}\usepackage{cmbright}\Huge\$

Multiply the radicals on top and on the bottom, then simplify.