Answer
$\dfrac{\sqrt{10}}{14}$
Work Step by Step
Recall, we are not allowed to have radicals in the denominator of a fraction. Using the properties of radicals, the given expression, $
\dfrac{2\sqrt{5}}{7\sqrt{8}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2\sqrt{5}}{7\sqrt{8}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}
\\\\=
\dfrac{2\sqrt{10}}{7\sqrt{16}}
\\\\=
\dfrac{2\sqrt{10}}{7\sqrt{(4)^2}}
\\\\=
\dfrac{2\sqrt{10}}{7\cdot4}
\\\\=
\dfrac{\cancel{2}\sqrt{10}}{7\cdot\cancel{2}(2)}
\\\\=
\dfrac{\sqrt{10}}{14}
.\end{array}
