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# If x <0 , then \sqrt{-x*|x|} equals 1. -x 2. -1 3. 1 4.

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VP
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18 Mar 2006, 21:20
vivek123 wrote:
Professor wrote:
vivek123 wrote:
This is my logic---->
We know that x<0, then -x > 0. In other words, -x*|x| = +x^2
so,
sqrt(-x*|x|) = sqrt(x^2)
= +x or -x. but since it is GIVEN that x < 0,

(For any sqrt, answer is always "+" or "-" ; but if some condition is given, we can arrive at whether "+" OR "-")

but we cannot have -x as one of the value of sqrt(x^2) because sqrt(x^2) has only one value that is x. any square under radical sign has only +ve value.

How do you say that? For example, "25" is a square of "5" & also of "-5".
sqrt(25) = +5 or -5. I didn't get your point.

lets see the following examples:

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

these two are different conditions. so,

from (I), the value of x = + or - 5
from (II), the value of x can only be +5.

i believe math experts like honghu and laxi are highly useful here. however, i found the following links to further clearification.
http://www.gmatclub.com/phpbb/viewtopic ... ght=#73232

further to my replies, i have seen somewhere in OG that sqrt (x) = +x only. i will post the same when i find.
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18 Mar 2006, 21:29
Professor wrote:
vivek123 wrote:
Professor wrote:
vivek123 wrote:
This is my logic---->
We know that x<0, then -x > 0. In other words, -x*|x| = +x^2
so,
sqrt(-x*|x|) = sqrt(x^2)
= +x or -x. but since it is GIVEN that x < 0,

(For any sqrt, answer is always "+" or "-" ; but if some condition is given, we can arrive at whether "+" OR "-")

but we cannot have -x as one of the value of sqrt(x^2) because sqrt(x^2) has only one value that is x. any square under radical sign has only +ve value.

How do you say that? For example, "25" is a square of "5" & also of "-5".
sqrt(25) = +5 or -5. I didn't get your point.

lets see the following examples:

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

these two are different conditions. so,

from (I), the value of x = + or - 5
from (II), the value of x can only be +5.

i believe math experts like honghu and laxi are highly useful here. however, i found the following links to further clearification.
http://www.gmatclub.com/phpbb/viewtopic ... ght=#73232

further to my replies, i have seen somewhere in OG that sqrt (x) = +x only. i will post the same when i find.

What is the difference between (I) & (II)? I guess we arrive on (II) from (i) itself.
I have a very uneasy feeling on this.
VP
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18 Mar 2006, 21:37
vivek123 wrote:
Professor wrote:
lets see the following examples:
(I) x^2 = 25
(II) x = square root 25

these two are different conditions. so,

from (I), the value of x = + or - 5
from (II), the value of x can only be +5.

i believe math experts like honghu and laxi are highly useful here. however, i found the following links to further clearification.
http://www.gmatclub.com/phpbb/viewtopic ... ght=#73232

further to my replies, i have seen somewhere in OG that sqrt (x) = +x only. i will post the same when i find.

What is the difference between (I) & (II)? I guess we arrive on (II) from (i) itself.
I have a very uneasy feeling on this.

if x^2 = 25, x can be both +ve and -ve but if x = square root (25) x can only be 5, not -5. thats it. i told you it is in OG but where? i am trying to find it. once i get it, i will let you know.
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18 Mar 2006, 22:26
Professor wrote:
vivek123 wrote:
Professor wrote:
vivek123 wrote:
This is my logic---->
We know that x<0, then -x > 0. In other words, -x*|x| = +x^2
so,
sqrt(-x*|x|) = sqrt(x^2)
= +x or -x. but since it is GIVEN that x < 0,

(For any sqrt, answer is always "+" or "-" ; but if some condition is given, we can arrive at whether "+" OR "-")

but we cannot have -x as one of the value of sqrt(x^2) because sqrt(x^2) has only one value that is x. any square under radical sign has only +ve value.

How do you say that? For example, "25" is a square of "5" & also of "-5".
sqrt(25) = +5 or -5. I didn't get your point.

lets see the following examples:

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

these two are different conditions. so,

from (I), the value of x = + or - 5
from (II), the value of x can only be +5.

i believe math experts like honghu and laxi are highly useful here. however, i found the following links to further clearification.
http://www.gmatclub.com/phpbb/viewtopic ... ght=#73232

further to my replies, i have seen somewhere in OG that sqrt (x) = +x only. i will post the same when i find.
i believe u have it mistaken. i'm sure i've seen cases contrary to your explanation for (II)
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19 Mar 2006, 04:02
Square root of 25 is 5 as far as Gmat is concerned( it can be -5 of course, but not in Gmat)

The question is x<0 ,sqr (-x * l x l= ?

let x be -2

sqr ( 2* l-2l)= sqr( 2*2)= sqr(4) = 2

since x is -2 , 2 is -x.

That is it.
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19 Mar 2006, 04:51
Square root of 25 is 5 as far as Gmat is concerned( it can be -5 of course, but not in Gmat)

This is something that I really wonder. It sounds like "whether" is preferred over "if" in GMAT

You guys might be correct, I'll really appreciate if you can PLEASE clarify on this part
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19 Mar 2006, 09:26
Square root of 25 is 5 as far as Gmat is concerned( it can be -5 of course, but not in Gmat)

You aren't right. The square root of a negative number isn't mathematically defined.

As Professor said:

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

Statement II says that x has the value 5 and nothing else. Per definition you can take the square root soleily of a positive number or 0. Negative values aren't defined.

The thing why we consider -5 and +5 in statement I is that a number squared always yields a positive value, you know that of course. In two we don't square a number, and if we would we already knew that x is positive since it is sqrt25.

Of course if you consider sqrt (x^2) x can be positive or negative.

Hope that clarifies
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19 Mar 2006, 18:19
The square root of a negative number isn't mathematically defined.

As Professor said:
(I) x^2 = 25
(II) x = square root 25

Statement II says that x has the value 5 and nothing else. Per definition you can take the square root soleily of a positive number or 0. Negative values aren't defined.

The thing why we consider -5 and +5 in statement I is that a number squared always yields a positive value, you know that of course. In two we don't square a number, and if we would we already knew that x is positive since it is sqrt25.

the important concept is: sqrt (x) has only one value i.e. +ve.

x = sqrt (25) = only 5.
x^2 = 25 = 5 or -5.
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19 Mar 2006, 19:52
HIMALAYA wrote:
The square root of a negative number isn't mathematically defined.

As Professor said:
(I) x^2 = 25
(II) x = square root 25

Statement II says that x has the value 5 and nothing else. Per definition you can take the square root soleily of a positive number or 0. Negative values aren't defined.

The thing why we consider -5 and +5 in statement I is that a number squared always yields a positive value, you know that of course. In two we don't square a number, and if we would we already knew that x is positive since it is sqrt25.

the important concept is: sqrt (x) has only one value i.e. +ve.

x = sqrt (25) = only 5.
x^2 = 25 = 5 or -5.
i really don't understand the thinking behind this. why would sqrt have only one value?
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20 Mar 2006, 01:13
I repeat

Square root of 25 in GMAT: 5 ,nothing else.

BUT if you wanna go and check high math books,you can see that it can be -5.

What I dont understand : Why you guys lose time with unimportant stuff. Look at my solution. The answer to the original question is -x. And that is it. It has nothing to do with sqrt of 25 = 5 or -5!

p.s: By the way, if is only correct if it is used to convey the meaning of a possibility. Whether is always correct when you talk about alternatives.
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20 Mar 2006, 07:35
I repeat

Square root of 25 in GMAT: 5 ,nothing else.

BUT if you wanna go and check high math books,you can see that it can be -5.

What I dont understand : Why you guys lose time with unimportant stuff. Look at my solution. The answer to the original question is -x. And that is it. It has nothing to do with sqrt of 25 = 5 or -5!

p.s: By the way, if is only correct if it is used to convey the meaning of a possibility. Whether is always correct when you talk about alternatives.
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20 Mar 2006, 11:07
guys, lets be polite and respectful to each other in expressing our views. its one's freedom whether to take the views expressed here.

I also agree with that SQRT (25) = 5. but the reason .

i believe Honghu can explain.
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20 Mar 2006, 23:39
Square root of any positive number is a positive number. When we say x^2=a, we know that x=+/-sqrt(a). You can see that sqrt(a) itself is positive, but x could be positive sqrt(a) or negative sqrt(a).

Using an example, say x^2=25. We know that x=+/-sqrt(25), where sqrt(25)=5.

Hope this helps.
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keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

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20 Mar 2006, 23:42
square root of a positive number is a positive number..

x^2 = 4, x = + or -2
if x = sqrt(4), x = 2
nothing else.
sqrt(-4) = 2i

so in this case.. the answer is sqrt(-x|x|)
since x is < 0,so pick x = -4, we have sqrt(-(-4)*|-4|)
==> 4

This is what I learnt at school.. Now I am totally lost if this IS WRONG.
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20 Mar 2006, 23:59
Just to End this discussion let me quote from the bible (OG-11, Page 126)

9. Absolute Value
The absolute value of x is denoted |x|, is defined to be x if x>=0 and â€“x is x<0. Note that sqrt(x^2) denotes that nonnegative square root of x^2 and so sqrt(x^2) = |x|

Following this answer of the question should be â€“x, as x is already negative and we need positive answer.

I hope this helps.
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21 Mar 2006, 00:43
believe2 wrote:
if x <0 , then sqrt (-x |x|) equals

1. -x
2. -1
3. 1
4. x
5. sqrt(x)

If x<0, the |x|=-x. sqrt(-x|x|)=sqrt((-x)^2)=-x.

Look at the options, you know that 2 and 3 can be thrown out right away. sqrt(x) is wrong because for GMAT only positive number can be inside a square root. Compare 1 and 4, you want a positive number, which would be -x since x is negative.
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21 Mar 2006, 04:37
HongHu wrote:
believe2 wrote:
if x <0 , then sqrt (-x |x|) equals

1. -x
2. -1
3. 1
4. x
5. sqrt(x)

If x<0, the |x|=-x. sqrt(-x|x|)=sqrt((-x)^2)=-x.

Look at the options, you know that 2 and 3 can be thrown out right away. sqrt(x) is wrong because for GMAT only positive number can be inside a square root. Compare 1 and 4, you want a positive number, which would be -x since x is negative.

I guess this is how I arrived at my answer -x
But I was totally confused with what is needed in GMAT etc.

Anyways, thanks Hong

Cheers
VP
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21 Mar 2006, 07:56
HongHu wrote:
Square root of any positive number is a positive number. When we say x^2=a, we know that x=+/-sqrt(a). You can see that sqrt(a) itself is positive, but x could be positive sqrt(a) or negative sqrt(a).

Using an example, say x^2=25. We know that x=+/-sqrt(25), where sqrt(25)=5.

Hope this helps.

i just want to be/make clear on why sqrt (25) = 5.

suppose x^2 = 25
x = sqrt (25) or - sqrt (25)
and we are here dealing with only "sqrt (25)".

therefore, sqrt (25) = 5

thank you honghu.
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21 Mar 2006, 09:33
I still dont understand..

isnt |x| just the positive value of the number x?
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21 Mar 2006, 09:41
willget800 wrote:
I still dont understand..

isnt |x| just the positive value of the number x?

Yes. But what if the x is -ve (say x = -2), then the absolute value of x is 2
x = -2
|x| = 2 = -(-2) = -x

For more gyan (Hindi word for knowledge) see..

http://www.purplemath.com/modules/absolute.htm
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