Answer
$3\sqrt[]{5}-5\sqrt[]{3}$
Work Step by Step
Using $a(b+c)=ab+ac$, or the Distributive Property, and the properties of radicals, the given expression, $
\sqrt[]{15}(\sqrt[]{3}-\sqrt[]{5})
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[]{15}(\sqrt[]{3})-\sqrt[]{15}(\sqrt[]{5})
\\\\=
\sqrt[]{15(3)}-\sqrt[]{15(5)}
\\\\=
\sqrt[]{(5\cdot3)(3)}-\sqrt[]{(5\cdot3)(5)}
\\\\=
\sqrt[]{3^2\cdot5}-\sqrt[]{5^2\cdot3}
\\\\=
3\sqrt[]{5}-5\sqrt[]{3}
.\end{array}
