I guess I thought that the square root of any positive number was positive and negative , as in ... x = +/- ( sqrt(y) ).

Solving an equation and simplifying a square root are two very different things.

When solving, you are finding all possible values which

*could* work. When simplifying, you need to simplify to one value; you can't start with one expression (for instance, the square root of nine) and end up with

*two* values (for instance, positive and negative three).

If you

*could* start with one value and then end up (after merely simplifying) with two, then major portions of mathematics would stop working.