Well, doing it that way makes more sense for your purpose. That, and it also allows it to equal -1.
Also, for anyone who for some reason doesn't believe me about the square root thing, here's some webpage that I found that talks about it.
The product of two positive numbers and the product of the same two negative numbers is the same positive number. This means the square root can be written as a positive and/or negative number. Mathematicians use principal square root when they are discussing positive square roots and negative square root when they refer to negative square roots. If the radical sign, √, is used:
√ = principal square root
- √ = negative square root
Well... that settles the manner

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