Answer
$\dfrac{1}{7}\sqrt{ab}$
Work Step by Step
Using $\sqrt{x}\cdot\sqrt{y}=\sqrt{xy}$ or the product rule of radicals, the given expression, $
\sqrt{\dfrac{1}{7}a}\cdot\sqrt{\dfrac{1}{7}b}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{1}{7}a\cdot\dfrac{1}{7}b}
\\\\=
\sqrt{\left(\dfrac{1}{7}\right)^2ab}
\\\\=
\dfrac{1}{7}\sqrt{ab}
.\end{array}
