Answer
$\sqrt[]{2ab}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{\sqrt[]{100ab}}{5\sqrt[]{2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{1}{5}\sqrt[]{\dfrac{100ab}{2}}
\\\\=
\dfrac{1}{5}\sqrt[]{50ab}
\\\\=
\dfrac{1}{5}\sqrt[]{25\cdot2ab}
\\\\=
\dfrac{1}{5}\sqrt[]{(5)^2\cdot2ab}
\\\\=
\dfrac{1}{5}\cdot5\sqrt[]{2ab}
\\\\=
\sqrt[]{2ab}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.