Answer
$2m^3n^2\sqrt{6n}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt{24m^6n^5}
,$ use the laws of exponents to simplify the radicand. Then, find a factor of the radicand that is a perfect power of the index. Finally, extract the root of the factor that is a perfect power of the root.
$\bf{\text{Solution Details:}}$
Factoring the expression that is a perfect power of the index and then extracting the root result to
\begin{array}{l}\require{cancel}
\sqrt{4m^6n^4\cdot6n}
\\\\=
\sqrt{(2m^3n^2)^2\cdot6n}
\\\\=
|2m^3n^2|\sqrt{6n}
.\end{array}
Since all variables are assumed to be positive, then,
\begin{array}{l}\require{cancel}
2m^3n^2\sqrt{6n}
.\end{array}
