Answer
$\dfrac{x\sqrt[]{2x}}{7y^2}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt[]{\dfrac{2x^3}{49y^4}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[]{\dfrac{x^2}{49y^4}\cdot2x}
\\\\=
\sqrt[]{\left( \dfrac{x}{7y^2} \right)^2\cdot2x}
\\\\=
\dfrac{x}{7y^2}\sqrt[]{2x}
\\\\=
\dfrac{x\sqrt[]{2x}}{7y^2}
.\end{array}
Note that all variables are assumed to have positive real numbers.
