Answer
$\sqrt[]{\dfrac{6s}{11t}}$
Work Step by Step
Using $\sqrt[a]{x}\sqrt[a]{y}=\sqrt[a]{xy}$, the given expression, $
\sqrt[]{\dfrac{2}{t}}\sqrt[]{\dfrac{3s}{11}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[]{\dfrac{2}{t}\cdot\dfrac{3s}{11}}
\\\\=
\sqrt[]{\dfrac{6s}{11t}}
.\end{array}