Answer
$\dfrac{\sqrt[]{7x}}{5y^{2}}$
Work Step by Step
Simplifying the given expression, $
\sqrt[]{\dfrac{21x^2y}{75xy^5}}
,$ results to
\begin{array}{l}\require{cancel}
\sqrt[]{\dfrac{\cancel{3}\cdot7x^{2-1}y^{1-5}}{\cancel{3}\cdot25}}
\\\\=
\sqrt[]{\dfrac{7x^{1}y^{-4}}{25}}
\\\\=
\sqrt[]{\dfrac{7x}{25y^{4}}}
\\\\=
\dfrac{\sqrt[]{7x}}{\sqrt[]{25y^{4}}}
\\\\=
\dfrac{\sqrt[]{7x}}{\sqrt[]{(5y^{2})^2}}
\\\\=
\dfrac{\sqrt[]{7x}}{5y^{2}}
.\end{array}
The simplified form of the given expression already has a rationalized denominator.
* Note that it is assumed that all variables represent positive numbers.