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## Main Question or Discussion Point

Hello everyone,

What is the square root of a square of a negative number equal to? For example: [itex]\sqrt{-1}^{2}[/itex]

It seems there are two possible ways of doing this, the problem is that I am getting two different answers using these two approaches i.e; We can first take the square of -1 and then take square root of the square of -1. This gives 1 as the answer. On the other hand, if we replace the radical sign by 1/2 as the exponent, we should then just be left with -1 as the answer. The correct answer, I think, is +1, but I can't figure out why there's an apparent contradiction...

Please help me understand where and why I am wrong.

Thank you!

What is the square root of a square of a negative number equal to? For example: [itex]\sqrt{-1}^{2}[/itex]

It seems there are two possible ways of doing this, the problem is that I am getting two different answers using these two approaches i.e; We can first take the square of -1 and then take square root of the square of -1. This gives 1 as the answer. On the other hand, if we replace the radical sign by 1/2 as the exponent, we should then just be left with -1 as the answer. The correct answer, I think, is +1, but I can't figure out why there's an apparent contradiction...

Please help me understand where and why I am wrong.

Thank you!