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Very SERIOUS

Expert replies
by orel » Wed Dec 03, 2008 6:23 am
hi folks..
on Kaplan prep guide I found he following explanation for Sq roots on GMAT.

But in real maths it is DIFFERENT! The Sq Root has always two values: + and -
It is very ambiguous!
May be it is typo on Kaplan method.....
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Source: — Problem Solving |

by niraj_a » Wed Dec 03, 2008 4:35 pm
i would go with what GMAT considers correct, simply because the GMAC is who ultimately decides your score.
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by cramya » Wed Dec 03, 2008 5:08 pm
Hope I am not mistaken here.

This is what is called the principal square root of a real number ( i.e. non negative square root of a real number).

I think this is what we mean when we say square root in the math world and GMAT.
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by orel » Wed Dec 03, 2008 5:17 pm
so, according to GMAC, the OA for the next question must be D

right?
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by orel » Wed Dec 03, 2008 5:17 pm
But the OA is A
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by cramya » Wed Dec 03, 2008 5:27 pm
It may sound a bit confusing. This is what my understanding is

When I say square root what I mean is

let say sqrt(16) = ?

We use +4 since if u consider 16 as (-4)^2 or (4)^2 sqrt(x^2) = |x|

If u take x=-4 or +4 u still get the square root as +4 only because u r taking the absolute value


In the problem above

a^2 = 4
sqrt(a^2) = sqrt(2) ^ 2 or sqrt(a^2) = sqrt(-2) ^ 2

|a| = 2 (since |2| or |-2| is 2)

Whenever u have modulus u have 2 cases when its positive and negative (nothing to do with square root since u have crossed that stage above)

so a=2 (or) -a=2 i.e a=-2

2 possible values


I hope I made sense here! Someone please feel free to jump in and correct me if I am mistaken.
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by lunarpower » Wed Dec 03, 2008 11:44 pm
here's the deal: you're talking about two different things.

when you have an OPERATOR SYMBOL, such as "√", that symbol will produce exactly ONE value.
for instance, √9 is just 3.
|-5| is just 5.
and so on.
notice, in these cases, that you're merely simplifying expressions; you are NOT solving EQUATIONS. in other words, there's no "=" sign in the middle of what you're dealing with; you're not finding the solutions of anything. just simplifying.

when you solve an EQUATION, there may well be more than one solution.
if you say x^2 = 9, there are two solutions: x = 3 and x = -3.
notice that i can say this without speaking of the "√" symbol at all!

indeed, the "√" symbol is DEFINED to refer only to the positive root. it is NOT defined to refer to either of the 2 solutions to the above equation.

hth.
Ron has been teaching various standardized tests for 20 years.

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by cramya » Wed Dec 03, 2008 11:46 pm
Thanks Ron! Much appreciated!
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by logitech » Thu Dec 04, 2008 12:12 am
Cramya, next time you thank Lunarpower, you can also try to click THANK YOU button. ( I have not been teasing you for a while so live with it) :) And also who is the ONLY person you thanked ? And what was it for ?hahahaha
LGTCH
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by orel » Thu Dec 04, 2008 7:31 am
Thanks to everybody!
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