#### Answer

$-\dfrac{5m^2\sqrt{6mn}}{n^2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
-\sqrt{\dfrac{150m^5}{n^3}}
,$ multiply the radicand by an expression equal to $1$ which will make the denominator a perfect power of the index.
$\bf{\text{Solution Details:}}$
Multiplying the radicand by an expression equal to $1$ which will make the denominator a perfect power of the index results to
\begin{array}{l}\require{cancel}
-\sqrt{\dfrac{150m^5}{n^3}\cdot\dfrac{n}{n}}
\\\\=
-\sqrt{\dfrac{150m^5n}{n^4}}
.\end{array}
Writing the radicand as an expression that contains a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
-\sqrt{\dfrac{25m^4}{n^4}\cdot6mn}
\\\\=
-\sqrt{\left( \dfrac{5m^2}{n^2} \right)^2\cdot6mn}
.\end{array}
Extracting the root of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
-\dfrac{5m^2}{n^2}\sqrt{6mn}
\\\\=
-\dfrac{5m^2\sqrt{6mn}}{n^2}
.\end{array}