#### Answer

$5\sqrt{14}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\sqrt{10}\sqrt{35}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{10(35)}
\\\\=
\sqrt{2\cdot5(5\cdot7)}
\\\\=
\sqrt{(5)^2\cdot2\cdot7}
\\\\=
\sqrt{(5)^2\cdot14}
\\\\=
5\sqrt{14}
\end{array}