| >> What does that have to do with sqrt(x) being positive by definition?
| >
| > Well, you seem to be following some rule I'm not aware of.
| > I'm trying to figure out what it is.
| > If -2 is a sqrt of 4, then sqrt(4) * sqrt(4)= 4
| > and also -sqrt(4) * -sqr(4)  = 4.
| > What's nearly wrong with that?
| 
| sqrt(4)*sqrt(4) can also be -4
| You simply multiply the negative root by the positive one.

Yep