Answer
$\dfrac{\sqrt {6xy}}{6y^2}$
Work Step by Step
To simplify the given expression, there should be no radicals in the denominator.
To achieve this, rationalize the denominator by multiplying $\sqrt{6y}$ to both the numerator and the denominator to obtain:
$=\dfrac{\sqrt x}{\sqrt {6y^3}} \cdot \dfrac{\sqrt {6y^3}}{\sqrt {6y^3}}$
$=\dfrac{\sqrt {6xy^3}}{\sqrt {36y^6}}$
$=\dfrac{\sqrt{y^2(6xy)}}{\sqrt {(6)^2(y^3)^2}}$
Take the square roots of the perfect squares:
$=\dfrac{y\sqrt {6xy}}{6y^3}$
Cancel out the common factor $y$ to obtain:
$=\dfrac{\sqrt {6xy}}{6y^2}$
