Answer
$-\dfrac{4k\sqrt{3z}}{z}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
-\sqrt{\dfrac{48k^2}{z}}
,$ 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}
-\sqrt{\dfrac{48k^2}{z}\cdot\dfrac{z}{z}}
\\\\=
-\sqrt{\dfrac{48k^2z}{z^2}}
.\end{array}
Rewriting the radicand using an expression that contains a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
-\sqrt{\dfrac{16k^2}{z^2}\cdot3z}
\\\\=
-\sqrt{\left(\dfrac{4k}{z}\right)^2\cdot3z}
.\end{array}
Extracting the root of the radicand that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
-\dfrac{4k}{z}\sqrt{3z}
\\\\=
-\dfrac{4k\sqrt{3z}}{z}
.\end{array}
