Answer
$9\sqrt{3}$
Work Step by Step
Using the properties of radicals, the given expression, $
5\sqrt{12}+3\sqrt{27}-2\sqrt{75}
,$ simplifies to
\begin{array}{l}\require{cancel}
5\sqrt{4\cdot3}+3\sqrt{9\cdot3}-2\sqrt{25\cdot3}
\\\\=
5\sqrt{(2)^2\cdot3}+3\sqrt{(3)^2\cdot3}-2\sqrt{(5)^2\cdot3}
\\\\=
5\cdot2\sqrt{3}+3\cdot3\sqrt{3}-2\cdot5\sqrt{3}
\\\\=
10\sqrt{3}+9\sqrt{3}-10\sqrt{3}
\\\\=
9\sqrt{3}
.\end{array}
