Answer
$15\sqrt{2}$
Work Step by Step
Extracting the factors that are perfect powers of the index, the given expression simplifies to
\begin{array}{l}\require{cancel}
\sqrt{50}+2\sqrt{18}+\sqrt{32}
\\\\=
\sqrt{25\cdot2}+2\sqrt{9\cdot2}+\sqrt{16\cdot2}
\\\\=
\sqrt{(5)^2\cdot2}+2\sqrt{(3)^2\cdot2}+\sqrt{(4)^2\cdot2}
\\\\=
5\sqrt{2}+2\cdot3\sqrt{2}+4\sqrt{2}
\\\\=
5\sqrt{2}+6\sqrt{2}+4\sqrt{2}
\\\\=
(5+6+4)\sqrt{2}
\\\\=
15\sqrt{2}
.\end{array}
