Answer
$\dfrac{2\sqrt{3}}{9}$
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{\sqrt{4}}{\sqrt{27}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{4}}{\sqrt{27}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}
\\\\=
\dfrac{\sqrt{4\cdot3}}{\sqrt{81}}
\\\\=
\dfrac{\sqrt{(2)^2\cdot3}}{\sqrt{(9)^2}}
\\\\=
\dfrac{2\sqrt{3}}{9}
.\end{array}