if I square a negative number, that makes it positive, right?
Squaring a negitive number produces the positive square of said number.
No, in fact there is a term for the answer you get it if you have to square a negative number... called imaginary.
Imaginary is shortened to the letter i. This i has a value of sqrt(-1).
Here are some simple examples of imaginary numbers:
sqrt(-4) = 4i
sqrt(-7x) = 7xi
Hope this helped some.