Answer
$\sqrt[]{15} - \sqrt[]{6}$
Work Step by Step
Using the Distributive Property and the properties of radicals, the given expression, $
\sqrt[]{3}\left( \sqrt{5}-\sqrt{2} \right)
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[]{3}\left( \sqrt{5} \right) - \sqrt[]{3}\left(\sqrt{2} \right)
\\\\=
\sqrt[]{3(5)} - \sqrt[]{3(2)}
\\\\=
\sqrt[]{15} - \sqrt[]{6}
.\end{array}