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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).

Crabzmatic
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  • This might be of interest. Similar: https://www.quora.com/Is-there-a-generalized-way-of-expanding-sqrt-a+sqrt-b-into-a-sqrt-c-such-that-c-is-an-expression-containing-no-square-roots – MathIsHard Nov 01 '17 at 00:33

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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.

Crabzmatic
  • 487