Answer
$6\sqrt{5}-6\sqrt{3}$
Work Step by Step
Using $a(b+c)=ab+ac$ or the Distributive Property and the properties of radicals, the given expression, $
\sqrt{3}(2\sqrt{15}-3\sqrt{4})
,$ is equivalent to
\begin{array}{l}\require{cancel}
(\sqrt{3})(2\sqrt{15})-(\sqrt{3})(3\sqrt{4})
\\\\=
2\sqrt{15(3)}-3\sqrt{4(3)}
\\\\=
2\sqrt{45}-3\sqrt{12}
\\\\=
2\sqrt{9\cdot5}-3\sqrt{4\cdot3}
\\\\=
2\sqrt{(3)^2\cdot5}-3\sqrt{(2)^2\cdot3}
\\\\=
2\cdot3\sqrt{5}-3\cdot2\sqrt{3}
\\\\=
6\sqrt{5}-6\sqrt{3}
.\end{array}
