#### Answer

$41\sqrt{2}$

#### Work Step by Step

Simplifying each term and then combining like terms, the given expression, $
9\sqrt{50}-4\sqrt{2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
9\sqrt{25\cdot2}-4\sqrt{2}
\\\\=
9\sqrt{(5)^2\cdot2}-4\sqrt{2}
\\\\=
9\cdot5\sqrt{2}-4\sqrt{2}
\\\\=
45\sqrt{2}-4\sqrt{2}
\\\\=
41\sqrt{2}
.\end{array}