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Folks, In GMAT,why do we consider (X^2)^1/2 as positive?(X

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Anna Rama
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Folks, In GMAT,why do we consider (X^2)^1/2 as positive?(X [#permalink] New post   29 Dec 2004, 15:24
Folks,

In GMAT,why do we consider (X^2)^1/2 as positive?(X is an integer)?
Is this for convenience?

If it is right then
(X^2)^1/2 = |X|
++++

Please let me know your thoughts?Rgds,

Anna



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Re: Folks, In GMAT,why do we consider (X^2)^1/2 as positive?(X [#permalink] New post   29 Dec 2004, 15:31
let's take (2^2)^1/2 = (4)^1/2 = -2 or +2 . Why do you say in GMAT we always consider it as positive ? Not sure if I understand ur question
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Re: Folks, In GMAT,why do we consider (X^2)^1/2 as positive?(X [#permalink] New post   29 Dec 2004, 23:36
banerjeea_98 wrote:
let's take (2^2)^1/2 = (4)^1/2 = -2 or +2 . Why do you say in GMAT we always consider it as positive ? Not sure if I understand ur question



banerjee,

(2^2)^1/2 = (4)^1/2 = sq root 4 = +2

the value of sq root 4 is only positive i.e. 2 not -2.
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Re: Folks, In GMAT,why do we consider (X^2)^1/2 as positive?(X [#permalink] New post   30 Dec 2004, 04:10
MA,

Would we not consider (-2)^2 = (2) ^2?Thus ideally (x^1/2)^2 has 2 roots:+x and -x. But from the OG problems that I have seen,we consider only the positive root.An example will be D.S. Q 260 on OG 10th edition.

Rgds,
Anna
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Re: Folks, In GMAT,why do we consider (X^2)^1/2 as positive?(X [#permalink] New post   30 Dec 2004, 08:40
MA, I disagree when u say square root of 4 is only +2. Every positive number has two square roots, one positive and one negative. Both 2 and
-2 are square roots of 4.

This can be a typical DS question: x is an integer, is x = 3 ?

1) x^2 = 9 .....Here we get 2 values +3 and -3 thus insufficient.


However, understanding Anna ques now, it is true that when we use a radical sign i.e. square root sign, by definition, it means the principal or positive sqaure root only, thus as Anna said:

(X^2)^1/2 = |X| for all real numbers X
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Re: Folks, In GMAT,why do we consider (X^2)^1/2 as positive?(X [#permalink] New post   30 Dec 2004, 09:21
Banerjee,

Thank you for your response.For folks who are interested in why we assume positive root for radical sign i.e. square root sign,please refer to the following link:
https://www.jamesbrennan.org/algebra/rad ... _roots.htm
++++

Quote:
To avoid confusion between the two we define the symbol (this symbol is called a radical) to mean the principal or positive square root.

The convention is:

For any positive number x,

(x)^1/2 is the positive root, and

-(x)^1/2 is the negative root.
+++

Rgds,
Anna
banerjeea_98 wrote:
MA, I disagree when u say square root of 4 is only +2. Every positive number has two square roots, one positive and one negative. Both 2 and
-2 are square roots of 4.

This can be a typical DS question: x is an integer, is x = 3 ?

1) x^2 = 9 .....Here we get 2 values +3 and -3 thus insufficient.


However, understanding Anna ques now, it is true that when we use a radical sign i.e. square root sign, by definition, it means the principal or positive sqaure root only, thus as Anna said:

(X^2)^1/2 = |X| for all real numbers X
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Re: Folks, In GMAT,why do we consider (X^2)^1/2 as positive?(X [#permalink] New post   30 Dec 2004, 18:11
banerjeea_98 wrote:
MA, I disagree when u say square root of 4 is only +2. Every positive number has two square roots, one positive and one negative. Both 2 and
-2 are square roots of 4.

This can be a typical DS question: x is an integer, is x = 3 ?

1) x^2 = 9 .....Here we get 2 values +3 and -3 thus insufficient.


However, understanding Anna ques now, it is true that when we use a radical sign i.e. square root sign, by definition, it means the principal or positive sqaure root only, thus as Anna said:

(X^2)^1/2 = |X| for all real numbers X




Banerjee and Anna Rama,


let me clearify with the following examples:

if (I) x^2=25
(II) x=square root 25


from (I), the value of x=+or -5

from (II), the value of x can only be +5.

i hope it is clear now.



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Re: Folks, In GMAT,why do we consider (X^2)^1/2 as positive?(X [#permalink]
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