Answer
$-9m\sqrt{2m}+5m\sqrt{m}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt{18m^3}-3m\sqrt{32m}+5\sqrt{m^3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{9m^2\cdot2m}-3m\sqrt{16\cdot2m}+5\sqrt{m^2\cdot m}
\\\\=
\sqrt{(3m)^2\cdot2m}-3m\sqrt{(4)^2\cdot2m}+5\sqrt{(m)^2\cdot m}
\\\\=
3m\sqrt{2m}-3m(4)\sqrt{2m}+5(m)\sqrt{m}
\\\\=
3m\sqrt{2m}-12m\sqrt{2m}+5m\sqrt{m}
\\\\=
-9m\sqrt{2m}+5m\sqrt{m}
.\end{array}
