Answer
$-17\sqrt{10}$
Work Step by Step
Using the properties of radicals, the given expression, $
2\sqrt{40}-7\sqrt{90}
,$ simplifies to
\begin{array}{l}\require{cancel}
2\sqrt{4\cdot10}-7\sqrt{9\cdot10}
\\\\=
2\sqrt{(2)^2\cdot10}-7\sqrt{(3)^2\cdot10}
\\\\=
2\cdot2\sqrt{10}-7\cdot3\sqrt{10}
\\\\=
4\sqrt{10}-21\sqrt{10}
\\\\=
-17\sqrt{10}
.\end{array}
