Answer
$-15\sqrt{2}-55\sqrt{5}$
Work Step by Step
Using the properties of radicals, the given expression, $
3\sqrt{8}-5\sqrt{20}-7\sqrt{18}-9\sqrt{125}
,$ simplifies to
\begin{array}{l}\require{cancel}
3\sqrt{4\cdot2}-5\sqrt{4\cdot5}-7\sqrt{9\cdot2}-9\sqrt{25\cdot5}
\\\\=
3\sqrt{(2)^2\cdot2}-5\sqrt{(2)^2\cdot5}-7\sqrt{(3)^2\cdot2}-9\sqrt{(5)^2\cdot5}
\\\\=
3\cdot2\sqrt{2}-5\cdot2\sqrt{5}-7\cdot3\sqrt{2}-9\cdot5\sqrt{5}
\\\\=
6\sqrt{2}-10\sqrt{5}-21\sqrt{2}-45\sqrt{5}
\\\\=
(6\sqrt{2}-21\sqrt{2})+(-10\sqrt{5}-45\sqrt{5})
\\\\=
-15\sqrt{2}-55\sqrt{5}
.\end{array}
