Answer
$3ab^2\sqrt{5}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt{45a^2b^4}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{9a^2b^4\cdot5}
\\\\=
\sqrt{(3ab^2)^2\cdot5}
\\\\=
3ab^2\sqrt{5}
.\end{array}
Note that all of the variables are assumed to represent non-negative real numbers.
