Answer
$\dfrac{11\sqrt{5}}{12}$
Work Step by Step
Using the properties of radicals, the expression $
\dfrac{\sqrt{20}}{3}+\dfrac{\sqrt{5}}{4}
$ is
\begin{array}{l}
\dfrac{\sqrt{4\cdot5}}{3}+\dfrac{\sqrt{5}}{4}
\\\\=
\dfrac{\sqrt{4\cdot5}}{3}+\dfrac{\sqrt{5}}{4}
\\\\=
\dfrac{2\sqrt{5}}{3}+\dfrac{\sqrt{5}}{4}
\\\\=
\dfrac{4\cdot2\sqrt{5}+3\cdot\sqrt{5}}{12}
\\\\=
\dfrac{8\sqrt{5}+3\sqrt{5}}{12}
\\\\=
\dfrac{11\sqrt{5}}{12}
.\end{array}
