Answer
$2\sqrt{2x}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt{32x}+\sqrt{2x}-\sqrt{18x}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{16\cdot2x}+\sqrt{2x}-\sqrt{9\cdot2x}
\\\\=
\sqrt{(4)^2\cdot2x}+\sqrt{2x}-\sqrt{(3)^2\cdot2x}
\\\\=
4\sqrt{2x}+\sqrt{2x}-3\sqrt{2x}
\\\\=
(4+1-3)\sqrt{2x}
\\\\=
2\sqrt{2x}
.\end{array}
