Is there any general way of finding root of a irrational number? (eg, getting $\sqrt2+\sqrt3$ from $\sqrt{5+2\sqrt6}$)

Question

for example:

$(\sqrt2+\sqrt3)^2 = 5+2\sqrt6$ is straightforward.
But how can we get $\sqrt2+\sqrt3$ from $\sqrt{5+2\sqrt6}$?

Is there any general method to do it?