Radical under Radical expression how to find the sum of $\sqrt{\frac54 + \sqrt{\frac32}} + \sqrt{\frac54 - \sqrt{\frac32}} $ ? Is there a method to solve these kind of equations ?

The general idea is to move along:
$$\sqrt{a}+\sqrt{r^2\,a} = \sqrt{a}+r\,\sqrt{a} = (1+r)\,\sqrt{a} = \sqrt{(1+r)^2\,a}$$
I am using the following systematic method as here, to first get the quotient:
$$r^2 = \frac{5/4+\sqrt{3/2}}{5/4-\sqrt{3/2}} = 49+20\sqrt{6} = (5+2\sqrt{6})^2$$
Therefore we have:
$$\sqrt{5/4-\sqrt{3/2}}+\sqrt{5/4+\sqrt{3/2}}= $$
$$\sqrt{(1+5+2\sqrt{6})^2\,(5/4-\sqrt{3/2})} = $$
$$\sqrt{(60+24\sqrt{6})\,(5/4-\sqrt{3/2})} = \sqrt{3}$$
