Aren't the negatives just indicating the direction? Whereas the pythagorean theorem is giving you a magnitude of the force. So if you move up with a force of 5 newtons or down with a force of 5 newtons, it's on the same axis so the magnitude of the force on that axis could be the same, but the direction would be different.
Of course, take this all with a grain of salt. I honestly don't remember from trig class, if you have three different axis' is it still square root or should it be cube root?