Answer
$\dfrac{n\sqrt{3n}}{11m^5}$
Work Step by Step
Using properties of radicals, the expression $
\sqrt{\dfrac{3n^3}{121m^{10}}}
$ simplifies to
\begin{array}{l}
\sqrt{\dfrac{n^2}{121m^{10}}\cdot3n}
\\\\=
\dfrac{n}{11m^5}\cdot\sqrt{3n}
\\\\=
\dfrac{n\sqrt{3n}}{11m^5}
.\end{array}