I don't understand one thing... the square of 1 = 1, the square of 2 = 4, the square of 3 = 9. Basically... a square is the number added to itself by the number of times it is. That is square of 2 is 2 added to itself 2 times.. so 4, and 3 added to itself 3 times makes it 9. Now take the negative number system... the square of -1 is -1 added to itself 1 time? and -2 is -2 added to itself 2 times? so doesn't that make square of -1 = -1? and the square of -2 equal to -4? so basically when you go to the root of the whole thing, this is what you should get. I know, i know the "rules" are that the square of a negative number is +ve... but why is this so? is there a proof to this?