Answer
$\dfrac{\sqrt[4]{ 7ts^2}}{s}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\sqrt[4]{\dfrac{7t}{s^2}}
,$ 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{7t}{s^2}\cdot\dfrac{s^2}{s^2}}
\\\\=
\sqrt[4]{\dfrac{7ts^2}{s^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}{s^4}\cdot 7ts^2}
\\\\=
\sqrt[4]{\left( \dfrac{1}{s} \right)^4\cdot 7ts^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{1}{s}\sqrt[4]{ 7ts^2}
\\\\=
\dfrac{\sqrt[4]{ 7ts^2}}{s}
.\end{array}
