# Why does calculator say that $\sqrt{4} = 2$? [duplicate]

Possible Duplicate:
Square roots — positive and negative

I know that the square roots of four are

• 2 because $2^2=4$
• and $-2$ because $(-2)^2=4$

Are there any conventions in considering primarily the positive square root or adding the $\pm$ symbol in the calculator screen would be a cost factor?

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## marked as duplicate by Asaf Karagila, Ayman Hourieh, Raskolnikov, Brian M. Scott, martiniOct 1 '12 at 11:31

There might be even better duplicates, but this one seems adequate. –  Asaf Karagila Oct 1 '12 at 11:20
By definition the symbol $\sqrt{x}$ denotes the non-negative square root of $x$. –  Brian M. Scott Oct 1 '12 at 11:30

The very same question could also apply to other functions (e.g. trigonometric functions). SQRT is defined as returning only the +ve value of the square root. Check here for a thorough discussion on this topic: http://forums.randi.org/archive/index.php/t-36241.html.

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If by "thorough" you mean "long and full of misconseptions", then by all means it's thorough. –  mrf Oct 1 '12 at 13:03