#### Answer

$\dfrac{5\sqrt{5}}{6}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\dfrac{2\sqrt{5}}{3}+\dfrac{\sqrt{5}}{6}
,$ change the terms to similar fractions by using the $LCD.$
$\bf{\text{Solution Details:}}$
To simplify the expression above, change the expressions to similar fractions (same denominator) by using the $LCD$. The $LCD$ of the denominators $
3
$ and $
6
$ is $
6
$ since it is the lowest number that can be exactly divided by the denominators. Multiplying the terms by an expression equal to $1$ that will make the denominator equal to the $LCD$ results to
\begin{array}{l}\require{cancel}
\dfrac{2\sqrt{5}}{3}\cdot\dfrac{2}{2}+\dfrac{\sqrt{5}}{6}
\\\\=
\dfrac{4\sqrt{5}}{6}+\dfrac{\sqrt{5}}{6}
\\\\=
\dfrac{(4+1)\sqrt{5}}{6}
\\\\=
\dfrac{5\sqrt{5}}{6}
.\end{array}