Answer
$\dfrac{6y\sqrt[]{y}}{x^2}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt[]{\dfrac{36y^3}{x^4}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[]{36y^3}}{\sqrt[]{x^4}}
\\\\=
\dfrac{\sqrt[]{36y^2\cdot y}}{\sqrt[]{x^4}}
\\\\=
\dfrac{\sqrt[]{(6y)^2\cdot y}}{\sqrt[]{(x^2)^2}}
\\\\=
\dfrac{6y\sqrt[]{y}}{x^2}
\end{array}
* Note that it is assumed that all variables represent positive numbers.