√25=5 or √25=+-5?

[tnaim]

this might seem like a simple question but then if you look at this example from GMATprep:
f x<0, then √(-x|x|) is
A. -x
B. -1
C. 1
D. x
E. √(x)

official answer is A






if you actually take -5 as an example to plug to the √(-x|x|) , you will see that you will end up with √25 and here the question becomes √25 is +-5 or just 5?
I have searched the internet for quite a bit and found conflicting opinions
Ron here says that √25 is just 5
https://www.manhattangmat.com/forums/if- ... t8539.html
enough resources on the internet say that √25 is +-5
https://mathforum.org/library/drmath/view/57877.html

my question thus is: what is √25? are there rules for when we consider √25=5 and other rules when √25=+-5? or is there just one answer all the time with no exceptions!!
thanks for the help!

[krazy800]

this might seem like a simple question but then if you look at this example from GMATprep:
f x<0, then √(-x|x|) is
A. -x
B. -1
C. 1
D. x
E. √(x)

official answer is A





if you actually take -5 as an example to plug to the √(-x|x|) , you will see that you will end up with √25 and here the question becomes √25 is +-5 or just 5?
I have searched the internet for quite a bit and found conflicting opinions
Ron here says that √25 is just 5
https://www.manhattangmat.com/forums/if- ... t8539.html
enough resources on the internet say that √25 is +-5
https://mathforum.org/library/drmath/view/57877.html

my question thus is: what is √25? are there rules for when we consider √25=5 and other rules when √25=+-5? or is there just one answer all the time with no exceptions!!
thanks for the help!

Tnaim:

In GMAT Land √25 = 5

when we have x=√25 then X can take +5 or -5

so when not equated to any variable, root of a number is positive!

lets try the above GMAT problem by choosing a value

Consider X=-2 (since X is negative)


|x|= 2

-x = 2

therefore

√(-x|x|) = √4 = 2

now note that 2 = -x

so A is ans

HTH!

[Patrick_GMATFix]

Hello Tnaim

You asked "Are there rules for when we consider root(25) = 5 and other rules when it's +-5?"

Basically, there are two situations:

• 1) if the GMAT presents a value as a root, that value is positive. If you're told that z=root(36), then z=6. If the GMAT already shows the value under a root, you're dealing with a positive root

• 2) If the GMAT presents the square (instead of the root), then you must consider both positive and negative solutions. If the GMAT states that z^2=36, then z can be +-6. In this case, z is not presented as a root. Instead, you're simply told that its square is 36.

In summary, if x=root(25), then x=5. On the other hand, if x^2=25, then x=+-5.

The question you presented is GMATPrep question 1051. 3 ways to solve as well as a step-by-step video solution of the question are available.

Good luck,
-Patrick

[uwhusky]

Same topic has been discussed recently: https://www.beatthegmat.com/gmatprep-problem-t58769.html

[tnaim]

Thank you all for the replies!!