I'm trying to simplify some expressions containing square roots, yet it seems that Mathematica has trouble dealing with them. For instance, consider the following:
Simplify[(1 + Sqrt[1 + z]) (-3 + Sqrt[5 + 4 Sqrt[1 + z] + z]) - z, Assumptions -> z > 0]
I do know that this is equal to 0, but
Simplify is unable to figure this out. (Using Series still allows me to verify this). Since all rooted values are positive, there should be no issues because of sign.
I have a bunch of other functions similarly shaped, which certainly contain significant simplifications, but for which I don't know how to figure out the result (and for which
Series is no help).