Answer
$\dfrac{\sqrt[4]{2yz^3}}{z}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\sqrt[4]{\dfrac{2y}{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[4]{\dfrac{2y}{z}\cdot\dfrac{z^3}{z^3}}
\\\\=
\sqrt[4]{\dfrac{2yz^3}{z^4}}
.\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[4]{\dfrac{1}{z^4}\cdot 2yz^3}
\\\\=
\sqrt[4]{\left( \dfrac{1}{z}\right)^4\cdot 2yz^3}
.\end{array}
Extracting the root of the radicand that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\dfrac{1}{z}\sqrt[4]{2yz^3}
\\\\=
\dfrac{\sqrt[4]{2yz^3}}{z}
.\end{array}
