Answer
$6\sqrt{5}-4$
Work Step by Step
Using $a(b+c)=ab+ac$ or the Distributive Property and the properties of radicals, the given expression, $
\sqrt{2}(3\sqrt{10}-\sqrt{8})
,$ is equivalent to
\begin{array}{l}\require{cancel}
(\sqrt{2})(3\sqrt{10})-(\sqrt{2})(\sqrt{8})
\\\\=
3\sqrt{2(10)}-\sqrt{2(8)}
\\\\=
3\sqrt{20}-\sqrt{16}
\\\\=
3\sqrt{4\cdot5}-\sqrt{16}
\\\\=
3\sqrt{(2)^2\cdot5}-\sqrt{(4)^2}
\\\\=
3\cdot2\sqrt{5}-4
\\\\=
6\sqrt{5}-4
.\end{array}
