I had thought that sqrt was defined as the positive square root just to avoid such apparent contradictions. If you want the negative square root, you have to specify it.
So, while 1^2=(-1)^2 => sqrt(1^2)=sqrt[(-1)^2], all that means is that 1 = 1, not that 1 = -1.
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I had thought that sqrt was defined as the positive square root just to avoid such apparent contradictions. If you want the negative square root, you have to specify it. So, while 1^2=(-1)^2 => sqrt(1^2)=sqrt[(-1)^2], all that means is that 1 = 1, not that 1 = -1.