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If x< 0, then squareroot (-x|x| ) is a) -x b) -1 c) 1 d)

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If x< 0, then squareroot (-x|x| ) is a) -x b) -1 c) 1 d) [#permalink]  15 Apr 2008, 09:59
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If x< 0, then squareroot (-x|x| ) is

a) -x
b) -1
c) 1
d) x
e) sqrt (x)
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Re: Gmatprep question :- DS sqrt [#permalink]  15 Apr 2008, 14:39

To explain, assume X is the positive value of x or X = -x

|x|= X

Since x < 0, -x = X (x with a positive sign) for example -(-1) = 1, -(-10) = 10 and so on..

sqrt (-x*|x|) = sqrt (X*X) = X which is equal to -x
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Re: Gmatprep question :- DS sqrt [#permalink]  15 Apr 2008, 15:20
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You can also plug in a number if that makes you more comfortable.

tmmyc wrote:
-x*lxl where x<0

Pick a number: x=-2

-x*lxl
-(-2)*l-2l
2*l-2l
2*2
4

sqrt(4) = 2
which is our above value of x multiplied by -1; hence the answer is -x.

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Re: Gmatprep question :- DS sqrt [#permalink]  15 Apr 2008, 17:34
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tmmyc wrote:
-x*lxl where x<0

Pick a number: x=-2

-x*lxl
-(-2)*l-2l
2*l-2l
2*2
4

sqrt(4) = 2
which is our above value of x multiplied by -1; hence the answer is -x.
[/quote]

Using this exact same method, what keeps us from getting sqrt(4) = -2? This would give us "x" or answer [D]. How do we know not to let sqrt(4) = +/-2 in certain problems?
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Re: Gmatprep question :- DS sqrt [#permalink]  16 Apr 2008, 06:24
bhatiagp wrote:
If x< 0, then squareroot (-x|x| ) is

a) -x
b) -1
c) 1
d) x
e) sqrt (x)

Put in a number for x. since x<0 make x=-2

-(-2)*|-2| --> 4 sqrt(4) = 2.

2=-(-2) or -x.
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Re: Gmatprep question :- DS sqrt [#permalink]  16 Apr 2008, 07:10
neat expln. fell for trap D.
agree with A. good one.
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Re: Gmatprep question :- DS sqrt [#permalink]  17 Apr 2008, 14:48
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Can someone please explain to me again why square root of 4 cannot be -2 as well as 2? Is it the square root of a number always have two roots, one positive and one negative?
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Re: Gmatprep question :- DS sqrt [#permalink]  17 Apr 2008, 15:17
lucyqin wrote:
Can someone please explain to me again why square root of 4 cannot be -2 as well as 2? Is it the square root of a number always have two roots, one positive and one negative?

Yea, I'm still waiting on this clarification as well.
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Re: Gmatprep question :- DS sqrt [#permalink]  19 Jun 2008, 07:09
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If you guys still need more explanations, see this link:
7-t59032
Hope this helps.
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Re: Gmatprep question :- DS sqrt [#permalink]  19 Jun 2008, 07:40
Thanks for the link dzyubam, +1.
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Re: Gmatprep question :- DS sqrt [#permalink]  19 Jun 2008, 11:44
lucyqin wrote:
Can someone please explain to me again why square root of 4 cannot be -2 as well as 2? Is it the square root of a number always have two roots, one positive and one negative?

True, by definition, square roots have a positive and negative value, but the GMAT only recognizes the positive root of a number.
Example: root4 = +2 (not -2)

However, if you are squaring a variable, the value for that variable will be a positive and negative value
Example: x^2 = 4 --> x = +/-2

Just something to keep in mind on test day!!
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Re: Gmatprep question :- DS sqrt   [#permalink] 19 Jun 2008, 11:44
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