square root symbol denotes only positive square roots?

Question

Is it true that when the √ sigh is used to denote square roots, only positive square roots are considered?

I am using Target Test Prep and they have hammered home this point multitudes of times. This changes te dimensions of questions, specially in DS, where for example x=√4 can only have the value 2 and not -2.

Bunuel · Answer

Yes. Mathematically,  \sqrt{...}  is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign ( \sqrt{...} ) always means non-negative square root.

https://gmatclub.com/forum/download/file.php?id=39502 
 The graph of the function f(x) = √x

Notice that it's defined for non-negative numbers and is producing non-negative results.

TO SUMMARIZE:
 When the GMAT (and generally in math) provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root.  That is:

\sqrt{9} = 3 , NOT +3 or -3;
 \sqrt {16} = 2 , NOT +2 or -2;

Notice that in contrast, the equation  x^2 = 9  has TWO solutions, +3 and -3. Because  x^2 = 9  means that  x =-\sqrt{9}=-3  or  x=\sqrt{9}=3 .

Hope it helps.

GmatKnightTutor · Answer

Yes.

Worth noting that √-2 is not something you need to consider on the GMAT as well. What's inside the √ will never be negative (at least on the GMAT).

-contact: gmatknight site | gmatclub dm

square root symbol denotes only positive square roots?

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