## Intermediate Algebra (12th Edition)

$\dfrac{11t^4\sqrt{2tu}}{u^{6}}$
$\bf{\text{Solution Outline:}}$ To rationalize the given radical expression, $\sqrt{\dfrac{242t^9}{u^{11}}} ,$ multiply the radicand by an expression equal to $1$ which will make the denominator a perfect power of the index. $\bf{\text{Solution Details:}}$ Multiplying the radicand 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{242t^9}{u^{11}}\cdot\dfrac{u}{u}} \\\\= \sqrt{\dfrac{242t^9u}{u^{12}}} .\end{array} Writing the radicand as an expression that contains a factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt{\dfrac{121t^8}{u^{12}}\cdot2tu} \\\\= \sqrt{\left(\dfrac{11t^4}{u^{6}}\right)^2\cdot2tu} .\end{array} Extracting the root of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \dfrac{11t^4}{u^{6}}\sqrt{2tu} \\\\= \dfrac{11t^4\sqrt{2tu}}{u^{6}} .\end{array}