Hello. From my calculator, I know that this is a true equality:
However, I simply cannot come up with the method used to "simplify" the first expression to arrive at the second expression (or vice versa). Could someone demonstrate or explain what I am missing?
Well, to be clear, seeing the equality, I can definitely prove that it is true, just like you showed.
I see that you can generalize it into an identity like this
I guess my point is: are there any other similar identities like this that would be useful in simplifying stacked square root expressions? I don't remember ever being taught this particular identity, although I'm not sure if it really occurs very often.