# Why is the square root of a number not plus or minus? [duplicate]

For example, $\sqrt{4}$. I've asked a bunch of people and I get mixed answers all the time, as to whether it is $-2$ and $+2$ or just $+2$.

How about if there's a negative in front of the square root sign, for example, $-\sqrt{4}$? Would that still be plus or minus or just minus?

## marked as duplicate by Rahul, choco_addicted, Strants, Claude Leibovici, WatsonMay 10 '16 at 7:07

• Note that $\sqrt {x^2}=|x|$, which is always positive. You cannot simply cancel the exponent. You have to make sure that you get a positive number. The graph of the square root function ($y=\sqrt x$) is defined to stay in the first quadrant. – Apurv May 10 '16 at 2:24
• $\sqrt {(-5)^2}=|-5|=5$, as per the definition I just gave in the previous comment. – Apurv May 10 '16 at 2:43