Answer
$\dfrac{x^2y}{\sqrt[]{2xy}}$
Work Step by Step
Rationalizing the numerator, the given expression, $
\sqrt[]{\dfrac{x^3y}{2}}
,$ is equivalent to
\begin{array}{l}
\sqrt[]{\dfrac{x^3y}{2}\cdot\dfrac{xy}{xy}}
\\\\=
\sqrt[]{\dfrac{x^4y^2}{2xy}}
\\\\=
\sqrt[]{\dfrac{(x^2y)^2}{2xy}}
\\\\=
\dfrac{x^2y}{\sqrt[]{2xy}}
.\end{array}