Anonymous Caller square roots I know the square root of -1 is i. Algebra II got that nicely drilled into my head, but is the square root of 1 also i, or is it just 1. I remember Ritsuko-san saying something about i awhile ago and have now become officially confused. Akagi Ritsuko The square root of 1 is 1. Proof: 1 x 1 = 1^2 = 1. Also, in case you were wondering, the square root of Zero is Zero. Note, however, that: -1 x -1 = 1 In fact, any negative number multiplied by another negative number is a positive number. Therefore, the square root of a negative number has no physical meaning (in artimatic, anyway). That's why the number i was invented, as more or less a placeholder. Akagi Ritsuko Interestingly enough, though, when the number i began being applied in the realm of Calculus (and gave birth to its own sub-discipline within mathematics), a number of formerly intractable problems found elegant solutions. The answers that lay just out of reach of real-number Calculus were reachable through a quick jaunt through "Imaginary Space" by way of Complex Calculus. Akagi Ritsuko It is all quite facinating, really. Truly elegant solutions arising from a unique perspective on the problem. Akagi Ritsuko What? What are you looking at me like that for? Eikichi Onizuka Calculus is pretty amazing. Any dude that can destroy planets is worthy of respect. Akagi Ritsuko I am afraid I have no idea what you are talking about..., and I think I would like to keep it that way.