Square root of X^2? : GMAT Quantitative Section
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Square root of X^2?

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16 Jun 2011, 21:36
Am I right in that the square root of X^2 is absolute value of x if we don't know whether x is negative or positive? Therefore, if we knew that x is negative, the square root of X^2 is -x? Thanks.
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Re: Square root of X^2? [#permalink]

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17 Jun 2011, 10:12
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I'd say yes..this concept is majorly tested in DS questions...
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Re: Square root of X^2? [#permalink]

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17 Jun 2011, 09:40
THe answer would be more circumstantial.

AFAIK, there is no hard and fast rule that GMAT specifies, to allow you to assume a specific behavior in these cases.

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Re: Square root of X^2? [#permalink]

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21 Jun 2011, 00:38
My understanding is the SQRT(x^2) = |x| since the square of an unknown yields +/- results. Therefore if x<0 then SQRT(x^2) is x=-a. Are you saying that a=-x?
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21 Jun 2011, 00:47
Sounds right to me too..
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Re: Square root of X^2? [#permalink]

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21 Jun 2011, 16:31
I have a simple question :

1) As per GMAT what is the value of x
x^2 = 1

x can have two values : +1 and -1 (that is logical) or
only one value : +1
x^2=1 ==> x = sqr. root(1) = 1...

.Got confused because in Kaplan it is mentioned as 2 values and I had read somewere in GMAT these equations have absolute values.

2)
x^4 = 1

Here definitely x will have 2 values : +1, -1

But not sure about the 1st case...
Please enlighten the GMAT logic on this...

x^2 =1 ==> x = +1,-1
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Re: Square root of X^2? [#permalink]

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21 Jun 2011, 16:54
Not sure this is GMAT logic or more general math logic, but here goes...

Lets say we investigate some squares: 1, 4, 9, 16, etc... Well how can we create these squares?
For 1: (1)^2 OR (-1)^2,
For 4: (2)^2 OR (-2)^2, etc...

Well when we undo the squares by taking the square root function then we create 2 solutions since there are 2 ways to make a square, ie 9 can be made by (3)^2 or (-3)^2. These returns are similar to absolute value function, since absolute value is basically distance on a number line AND all distances are positive. Since there are 2 ways to go on a number line (left or right) we have 2 solution possibilities for the absolute value. Therefore sqrt(x^2)=|x|. Hope that helps.
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Re: Square root of X^2? [#permalink]

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26 Jun 2011, 11:12
Unless the GMAT has a general policy, or a specific question states so, all you can do in situations like this is to state the correct math answer:

$$sqrt(x^2) = +/- x$$

(That is, unless you know x is supposed to be positive or negative.)
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Re: Square root of X^2? [#permalink]

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02 Jul 2011, 04:19
Yes sqrt of x^2 is |x| unless specified otherwise
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Re: Square root of X^2? [#permalink]

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02 Jul 2011, 14:37
yes it is...go to gmat club math book and look at the chapter of inequalitites...explicitly states so...
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Re: Square root of X^2? [#permalink]

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07 Jul 2011, 07:43
Yes, so now let's think about how the GMAT guys might test this concept through a question.

What if GMAT guys asked you:

what is [sqrt(x^2) ] / x ?

You might think...well, sqrt just means raising to the 1/2 power....so that woudl be x^(2 * 1/2) = x^1

And since you're dividing by x, then your answer would be 1.

The answer here would be |x| / x

Please see this video for more detailed explanation. (For members)
Re: Square root of X^2?   [#permalink] 07 Jul 2011, 07:43
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