#### Answer

$\dfrac{-8\sqrt{3k}}{k}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\dfrac{-8\sqrt{3}}{\sqrt{k}}
,$ 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{-8\sqrt{3}}{\sqrt{k}}\cdot\dfrac{\sqrt{k}}{\sqrt{k}}
\\\\=
\dfrac{-8\sqrt{3}(\sqrt{k})}{(\sqrt{k})^2}
\\\\=
\dfrac{-8\sqrt{3}(\sqrt{k})}{k}
.\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{-8\sqrt{3(k)}}{k}
\\\\=
\dfrac{-8\sqrt{3k}}{k}
.\end{array}