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D01-13

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Re: D01-13 [#permalink]

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New post 31 May 2017, 09:13
Can someone please provide the logic behind not taking the negative root for '√9=3, NOT +3 or -3;'
Is this mentioned anywhere int the OG or any other official material?
How do we know the GMAT doesn't consider the negative root ?

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New post 31 May 2017, 10:20
AllenF wrote:
Can someone please provide the logic behind not taking the negative root for '√9=3, NOT +3 or -3;'
Is this mentioned anywhere int the OG or any other official material?
How do we know the GMAT doesn't consider the negative root ?


This is explained many times. \(\sqrt{}\) denotes a function. Mathematically the square root function cannot give negative result.

OFFICIAL GUIDE:
\(\sqrt{n}\) denotes the positive number whose square is n.

Piece of advice, people here, experts/tutors, are here to help students, not to deceive them. So, if you see the same thing repeated many times by experts/tutors you should now that it's true.
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D01-13 [#permalink]

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New post 31 May 2017, 19:33
Bunuel wrote:
CristianJuarez wrote:
stan3544 wrote:
And here we go again. Sometimes i feel as if GMAT has it's own version of math that goes against universal one. I understand that on verbal there can be a whole lot of inerprteations of rules, simply because it is VERBAL, as in not a precise science which is basically a human imagination. But math has to be precise. And now, according to e-GMAT -b^m if m is even --> positive number and you are stating that −2^4=−16 and i made a whole lot of mistakes when practicing quant from both OG and scholaranium that involved sqr.root of a number, because i didn't include the negative value as well. Can comeone give a link or a screenshot of an OG question where when we take sqr root we don't consider the negative value?


The gmat doesn't have its own version of math. The square root is a function, that's why it is always positive. As a function, it can't take a positive and a negative value (if it did, it wouldn't be a function, you can look at the graph to check that out).

When you solve x^2 = 4, applying the square root function and assuming two results for x is incorrect, because you would only get x = 2. The formal and correct method is:
x^2 = 4
x^2 - 4 =0
(x + 2)(x - 2)=0 and from here get both results for x.


That's correct. + 1.

Another way of solving x^2 = 4 would be:

\(x = \sqrt{4}=2\) or \(x = -\sqrt{4}=-2\).


Yes, actually I'd like to correct myself, I hope it isn't more confusing.

Bunuel's solution applying square root function comes from the fact that the function f(x)=x^2 allows x to take positive or negative values (or 0):

I don't have 5 posts so I can't include the image :( , please search for it on google.

Meanwhile, the function \(f(x)= \sqrt{x}\) doesn't (this is why square root is always positive):

(check image on google)

So, if people want to solve this excercise by applying square root function, you must consider that this is incorrect:

\(x^2=4\) Apply \(\sqrt{}\)
\(\sqrt{x^2}=\sqrt{4}\)
\(x = \sqrt{4}\)
\(x=2\) or \(x= -2\)

It is incorrect because \(\sqrt{4}\) is always 2 and you lost a solution in the process.

So, you have to consider that mathemathically, \(\sqrt{x^2} = |x|\). This is only because \(f(x)=x^2\) can take a positive or a negative value for x (or 0 of course). Indeed, this doesn't mean the square root takes a positive or a negative solution, its always positive (or zero)!! (remember, \(|x|\) is always \(>= 0\) for any value of \(x\)).

You can check it out like this:
\(\sqrt{4} = \sqrt{2^2}= |2|=2, not -2!!\) or:
\(\sqrt{4} = \sqrt{(-2)^2}= |-2|=2, not -2!!\) It's impossible to get to \(-2\) like that

So the correct process by applying square root function is:
\(x^2=4\) Apply \(\sqrt{}\)
\(\sqrt{x^2}=\sqrt{4}\)
\(|x| = 2\)
\(x=2\) or \(x= -2\)

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New post 18 Aug 2017, 13:43
I think this is a high-quality question and I agree with explanation.

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Re: D01-13 [#permalink]

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New post 16 Nov 2017, 01:36
How do we know even root in GMAT is always positive ?

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New post 16 Nov 2017, 01:38

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Re D01-13 [#permalink]

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New post 21 Nov 2017, 00:04
I think this is a high-quality question and the explanation isn't clear enough, please elaborate.

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New post 21 Nov 2017, 00:07

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Re: D01-13   [#permalink] 21 Nov 2017, 00:07

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