Answer
$x^{4}y^{3}\sqrt{y}$
Work Step by Step
Extracting the factors that are perfect roots of the given index, the given expression, $
\sqrt{x^{8}y^{7}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{x^{8}y^{6}\cdot y}
\\\\=
\sqrt{(x^{4}y^{3})^2\cdot y}
\\\\=
x^{4}y^{3}\sqrt{y}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.