Why is the solution to $x-\sqrt 4=0$ not $x=\pm 2$? 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?

Actually while solving a quadratic equation we drop one step to short the answer or to save time whatever it may be. 
THE STEP IS: $$x^2-4=0\tag{Step $1$}$$ $$x^2=4\tag{Step $2$}$$ $$x=\pm\sqrt4\tag{Step $3$}$$ $$x=\pm2\tag{Step $4$}$$ In our solution we drop the $3^{rd}$ step. Actually the thing is that as the $(+)$ sign change side as $(-)$ and $(\times)$ sign change side as $(\div)$. Similarly the $(^2)$[square] sign change side as $(\pm\sqrt.)$
