Answer
$\dfrac{11t^4\sqrt{2tu}}{u^{6}}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
