Answer
$6\sqrt[]{10}-12\sqrt[]{15}$
Work Step by Step
Using the Distributive Property and the properties of radicals, the given expression, $
3\sqrt[]{5}(\sqrt[]{8}-2\sqrt[]{12})
,$ simplifies to
\begin{array}{l}\require{cancel}
3\sqrt[]{5}(\sqrt[]{8})-3\sqrt[]{5}(2\sqrt[]{12})
\\\\=
3\sqrt[]{5(8)}-3(2)\sqrt[]{5(12)}
\\\\=
3\sqrt[]{40}-6\sqrt[]{60}
\\\\=
3\sqrt[]{4\cdot10}-6\sqrt[]{4\cdot15}
\\\\=
3\sqrt[]{(2)^2\cdot10}-6\sqrt[]{(2)^2\cdot15}
\\\\=
3\cdot2\sqrt[]{10}-6\cdot2\sqrt[]{15}
\\\\=
6\sqrt[]{10}-12\sqrt[]{15}
.\end{array}
