[yorwba]

For x = -i, square(x) = -1, sqrt(square(x)) = i. Meanwhile, abs(x) = 1. You're right that it simplifies to abs(x) for real x, but that no longer holds for arbitrary complex values.

[NooneAtAll3]

for arbitrary complex values sqrt() gives 2 answers with +- signs

so sqrt(square(-i)) = +-i, one of which is x

[syockit]

I've never seen a CAS that gives two answers for sqrt. Mathematica doesn't, sympy doesn't, and IIRC Maxima also doesn't.

[Armisael16]

The sqrt function returns the principle square root, not both. That’s true for all numbers, positive, negative, and complex alike.