Answer
$4\sqrt[]{3}-\sqrt{6}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt[]{3}(\sqrt{16}-\sqrt{2})
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[]{3(16)}-\sqrt{3(2})
\\\\=
\sqrt[]{48}-\sqrt{6}
\\\\=
\sqrt[]{16\cdot3}-\sqrt{6}
\\\\=
\sqrt[]{(4)^2\cdot3}-\sqrt{6}
\\\\=
4\sqrt[]{3}-\sqrt{6}
.\end{array}
Note that all variables are assumed to have positive real numbers.