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Professor wrote: vivek123 wrote: Professor wrote: vivek123 wrote: A) -x ? I'll explain if correct  seems you have correct OA. but how? could you explain? 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, answer should be "-x". (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.
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old_dream_1976 wrote: vivek123 wrote: Professor wrote: vivek123 wrote: A) -x ? I'll explain if correct seems you have correct OA. but how? could you explain? 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, answer should be "-x". (For any sqrt, answer is always "+" or "-" ; but if some condition is given, we can arrive at whether "+" OR "-") I am with you untill sqrt(-x*|x|) = sqrt(x^2) = +x or -x. so sqrt(-x*|x|) is -ve or +ve and its absolute value is |x| x or -x how do you conclude that the value of the expression sqrt(-x*|x|) is -x? OD,
Frankly speaking, I'm not very comfortable with this problem. Ideally, answer should be "+/-x", but since it was already mentioned that x<0, (and most important: answer choice has both +x & -x, WE HAVE TO SELECT ONE CHOICE) the value that I selected is "-x"
For example, if we are solving sqrt(a) for something like age of a person, -ve value wouldn't make sense, we have to select +ve value.
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lets plug in numbers
ie x=-2
-(-2) * abs(-2)= 2+2=4
sqrt (4)=+/-2
just because x<0 doesnt mean the value of the equation is less than zero
hence this is a messsed up q.
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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,
answer should be "-x".
(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
http://www.jamesbrennan.org/algebra/rad ... _roots.htm
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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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,
answer should be "-x".
(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=#73232http://www.jamesbrennan.org/algebra/rad ... _roots.htmfurther 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.
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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=#73232http://www.jamesbrennan.org/algebra/rad ... _roots.htmfurther 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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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,
answer should be "-x".
(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=#73232http://www.jamesbrennan.org/algebra/rad ... _roots.htmfurther 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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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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INSEAD1979 wrote: 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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INSEAD1979 wrote: 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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allabout 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.
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HIMALAYA wrote: allabout 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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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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INSEAD1979 wrote: 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. If it's unimportant you don't have to bother replying the thread.
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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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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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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.
Please explain!!!!!!!!!!!!!!!!
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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 –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 –x, as x is already negative and we need positive answer.
I hope this helps.
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Re: absolute value [#permalink]
 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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Re: absolute value [#permalink]
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
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Re: absolute value
[#permalink]
21 Mar 2006, 04:37
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