kaplan error in CAT?

[uchicago]

i got this question on the kaplan CAT; i think they have it wrong because the square roots can be either positive or negative, so D is the correct choice.

anything i'm missing?

[linisha]

http://mathworld.wolfram.com/SquareRoot.html


Read through that link to understand what a "square root" actually means.
Hope that helps.

[Dimas]

Read the ETS math review, you will find that square root of 16 is 4, not +-4

[uchicago]

the above is from the math review i saw here doesn't seem to restrict square roots to just positive. this is from page 10, is there somewhere else to look? or i guess if we want -4, it would be -(sq rt 16), which seems circuitous.

anyway-- i'm sure the real GRE won't ask such an ambiguous question.

[Dimas]

It may ask this question, because it touches the gist of the meaning of the square root operator. I can see in the review, as I told you that, a solution of x^2 = N has two roots:
SQR(N) and -SQR(N). This means that, SQR(N) is positive and -SQR(N) is negative. This dispells any doubt that SQR(N) is -- strictly -- positive. I always remember my highschool teacher saying that:

Never say x^2 = 9 ==> x=+- 3. You should say: x= +- SQR(9) = +- 3.

Another mathematical proof is that the function y = x^0.5 is defined only for x>=0. While x is strictly positive, x^(any real number) is strictly positive. If x^0.5 itself yields positive and negative functions, then this will immidietly be refuted by the fact that all mathematics books define the function y=x^0.5 as a one-curve single-x-y mapping function.

In sum, square root of 16 is STRICTLY positive and equals 4. If X^2=16 then X= plus or minus the square root of 16 or plus or minus 4. ETS will most likely put this question on their favorite list because we are still debating it so far.

May the root be with you

[Ivo]

ETS official guide 10th edition:
p. 37
which of the following statements are true?

(b)square root of 16 = 4

(g)square root of 9 is less than 0

answers:

b is true.
g is not true.

following from this, one would say that square root of a number must be only positive. Because if it was not, then (b) could not be true (it would be either positive or negative, thus not meeting the condition as set in the problem for being true).

the bottom line of this it that for ETS square root of a number is always positive - no matter whether we agree with it theoretically or not.

ETS is the All Mighty (and most likely they've got it right even in terms of theory).

[engsamah]

I agree with Ivo. and I don't think it's an ambiguous question. (sqr rt 16) can not be -4, you say +(sq rt 16) if you want both probabilities. So nothing wrong with the question. This is how we studied it in CS.

[Dimas]

Agree with Sama7. Let's close it for the moment and announce it resounding:

A SQUARE ROOT OF A POSITIVE NUMBER IS A POSITIVE NUMBER

ok.

[Holden_Caulfield]

ETS GRE preparation book 10th edition, p. 37, line 20
"For example, a square root of 16 is 4 because 4^2=16. Another square root of 16 is -4 because (-4)^2=16."
It means that 16^0.5 != "square root of 16" - keep this in mind!

[soumyajayaraman]

when u have sq root of a number , always take it to be positive
example:

column a
sq root 4


column b
sq root 8

column b will be greater ... but if u have the following question

x square = 100
column a
x
column b
10

answer for that is d