#### Answer

$5y^4\sqrt{7}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\sqrt{175y^8}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{25y^8\cdot7}
\\\\=
\sqrt{(5y^4)^2\cdot7}
\\\\=
5y^4\sqrt{7}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.