## Intermediate Algebra (12th Edition)

$\dfrac{\sqrt[4]{ 7ts^2}}{s}$
$\bf{\text{Solution Outline:}}$ 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}