Formula for square root inside a square root

Question

I am trying to remember a formula from high school about nested square roots. It goes something like this:

$\sqrt{\frac{a+\sqrt{b}}{c}} = \sqrt{\frac{?}{?}} \pm \sqrt{\frac{?}{?}} $

This formula is supposed to eliminate nested squares, so there are only a,b,c inside squares on right side. I also remember calling it Lagrange formula (not sure).

Answer 1

Thanks to -Math4Life, formula i was looking is:

$\sqrt{a \pm \sqrt{b}} = \sqrt{\frac{a + \sqrt{a^2 -b}}{2}} \pm \sqrt{\frac{a-\sqrt{a^2-b}}{2}} $

Although it doesn't remove the nested square, it is often useful as $a^2-b$ can be a perfect square.