Answer
$\dfrac{-4\sqrt{13m}}{m}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\dfrac{-4\sqrt{13}}{\sqrt{m}}
,$ multiply both the numerator and the denominator by the expression equal to the denominator.
$\bf{\text{Solution Details:}}$
Multiplying both the numerator and the denominator by the expression equal to the denominator results to
\begin{array}{l}\require{cancel}
\dfrac{-4\sqrt{13}}{\sqrt{m}}\cdot\dfrac{\sqrt{m}}{\sqrt{m}}
\\\\=
\dfrac{-4\sqrt{13}(\sqrt{m})}{(\sqrt{m})^2}
\\\\=
\dfrac{-4\sqrt{13}(\sqrt{m})}{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{-4\sqrt{13(m)}}{m}
\\\\=
\dfrac{-4\sqrt{13m}}{m}
.\end{array}
