Answer
$5\sqrt{3}-5\sqrt{7}$
Work Step by Step
Using the Distributive Property, the given expression, $
\sqrt{5}(\sqrt{15}-\sqrt{35})
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{5}(\sqrt{15})-\sqrt{5}(\sqrt{35})
.\end{array}
Using the properties of radicals, the expression above simplifies to
\begin{array}{l}\require{cancel}
\sqrt{5(15)}-\sqrt{5(35)}
\\\\=
\sqrt{75}-\sqrt{175}
\\\\=
\sqrt{25\cdot3}-\sqrt{25\cdot7}
\\\\=
\sqrt{(5)^2\cdot3}-\sqrt{(5)^2\cdot7}
\\\\=
5\sqrt{3}-5\sqrt{7}
.\end{array}
