>>12897395Let me state it very simply, his qualm is that sqrt4 is equal to 2, whereas -2 is also a solution to the equation he wrote.
What he is missing however is that sqrt4 is in fact equal to both positive and negative 2, meaning that ab=mn^2 does in fact imply that mn=sqrtab, as sqrtab= +-mn
Of course in most contexts the negative solution is ignored and you take only positive root, I.e the principal root, as an answer, but technically the root has two solutions.
Look into why the square root function has a restricted range, you might want to also read this
https://mathworld.wolfram.com/PrincipalSquareRoot.html 
