Answer
$-36\sqrt{2}$
Work Step by Step
Using the properties of radicals, the given expression, $
4\sqrt{18}-6\sqrt{50}-3\sqrt{72}
,$ simplifies to
\begin{array}{l}\require{cancel}
4\sqrt{9\cdot2}-6\sqrt{25\cdot2}-3\sqrt{36\cdot2}
\\\\=
4\sqrt{(3)^2\cdot2}-6\sqrt{(5)^2\cdot2}-3\sqrt{(6)^2\cdot2}
\\\\=
4\cdot3\sqrt{2}-6\cdot5\sqrt{2}-3\cdot6\sqrt{2}
\\\\=
12\sqrt{2}-30\sqrt{2}-18\sqrt{2}
\\\\=
-36\sqrt{2}
.\end{array}
