Answer
$\dfrac{2\sqrt{5rm}}{m^2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\dfrac{2\sqrt{5r}}{\sqrt{m^3}}
,$ multiply the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index.
$\bf{\text{Solution Details:}}$
Multiplying the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index results to
\begin{array}{l}\require{cancel}
\dfrac{2\sqrt{5r}}{\sqrt{m^3}}\cdot\dfrac{\sqrt{m}}{\sqrt{m}}
.\end{array}
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel}
\dfrac{2\sqrt{5rm}}{\sqrt{m^3(m)}}
\\\\=
\dfrac{2\sqrt{5rm}}{\sqrt{m^4}}
\\\\=
\dfrac{2\sqrt{5rm}}{\sqrt{(m^2)^2}}
.\end{array}
Extracting the root of the radicand that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\dfrac{2\sqrt{5rm}}{m^2}
.\end{array}
