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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.
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.
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.
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.
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.
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.
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?
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.
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.
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. _________________
Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.
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.
Re: absolute value [#permalink]
20 Mar 2006, 23:43
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. _________________
Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.
Re: absolute value [#permalink]
21 Mar 2006, 03:37
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.
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)".
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