The expression $\pm\sqrt x \pm \sqrt x$ has three values: $[2\sqrt x,-2\sqrt x, 0]$. One might rewrite the initial expression as $2\sqrt x$, but this gets rid of the 0 value. Is this only applicable to principal square root, or is there another explanation?
In respect to notation, it feels awkward and incorrect to write the original expression over the latter(due to the contents of the root being identical; I have an inclination to combine the terms). However, I need this third value. Is it correct notation to write the first expression, or is there another way that I am missing?
Note: I ask this because I am looking for expressions that have exactly 3 possible values. This is the only kind I could yet construct. Any other example would be appreciated.