TITLE: Why is the solution to $x-\sqrt 4=0$ not $x=\pm 2$?
QUESTION [6 upvotes]: If the equation is $x-\sqrt 4=0$, then $x=2$.
If the equation is $x^2-4=0$, then $x=\pm 2$.
Why is it not $x=\pm 2$ in the first equation?

REPLY [2 votes]: The function $\sqrt. $ returns only non-negative numbers. And its range is [0,$\infty$) that's why $\sqrt4 = 2$ and $\sqrt4 ≠ ±2$