How to simplify $\sqrt{2+\sqrt{3}}$ $?$ 
Simplify $\dfrac{2\left(\sqrt2 + \sqrt6\right)}{3\sqrt{2+\sqrt3}}$ 

The answer to this question is $\frac{4}{3}$ in a workbook.
How would I simplify $\sqrt{2+\sqrt3}$ $?$ If it was something like $\sqrt{3 + 2\sqrt2}$ ,  I would have simplified it as follows: 
$\sqrt{3 + 2\sqrt2}$ $=$ $\sqrt{(\sqrt2)^2 + 2(\sqrt2)(1) + (1)^2}$ $=$
$\sqrt{(\sqrt2 + 1)^2}$  $=$
$\sqrt2 + 1$
But I can't simplify $\sqrt{2+\sqrt3}$  like that as $2+\sqrt3$ is can't be written as squares of two numbers. Is there any other method?

Note that$$\left(\frac{2\left(\sqrt2+\sqrt6\right)}{3\sqrt{2+\sqrt3}}\right)^2=\frac{4\left(8+4\sqrt3\right)}{9\left(2+\sqrt3\right)}=\frac{16}9=\left(\frac43\right)^2.$$
