>>12572379>>12572359Sqrt(36) is defined as a positive solution to x^2=36. There is no any axiom or a theorem which says sqrt(ab)=sqrt(a)sqrt(b), OP's post is a counterexample to it in fact.
sqrt(ab)=sqrt(a)sqrt(b) can be proven to hold only when a and b are greater than or equal to zero.
There is nothing paradoxical about that behaviour. Say, does the noncommutativity of quaternions bother you?
