#### Answer

$3x^2y\sqrt[]{7}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\sqrt[]{63x^4y^2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[]{9x^4y^2\cdot7}
\\\\=
\sqrt[]{(3x^2y)^2\cdot7}
\\\\=
3x^2y\sqrt[]{7}
.\end{array}
Note that all of the variables are assumed to represent non-negative real numbers.