Answer
$33\sqrt{2}$
Work Step by Step
Using the properties of radicals, the given expression, $
7\sqrt{32}+5\sqrt{2}
,$ simplifies to
\begin{array}{l}\require{cancel}
7\sqrt{16\cdot2}+5\sqrt{2}
\\\\=
7\sqrt{(4)^2\cdot2}+5\sqrt{2}
\\\\=
7\cdot4\sqrt{2}+5\sqrt{2}
\\\\=
28\sqrt{2}+5\sqrt{2}
\\\\=
33\sqrt{2}
.\end{array}
Note that all of the variables are assumed to represent non-negative real numbers.
