Answer
$-4|a|\sqrt{a}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt{36a^3}-\sqrt{144a^3}+\sqrt{4a^3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{36a^2\cdot a}-\sqrt{144a^2\cdot a}+\sqrt{4a^2\cdot a}
\\\\=
\sqrt{(6a)^2\cdot a}-\sqrt{(12a)^2\cdot a}+\sqrt{(2a)^2\cdot a}
\\\\=
|6a|\sqrt{a}-|12a|\sqrt{a}+|2a|\sqrt{a}
\\\\=
6|a|\sqrt{a}-12|a|\sqrt{a}+2|a|\sqrt{a}
\\\\=
-4|a|\sqrt{a}
.\end{array}
