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If x <0 , then \sqrt{-x*|x|} equals 1. -x 2. -1 3. 1 4. : GMAT Problem Solving (PS) - Page 2

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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.

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.

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.

Anyways, thanks Hong

Cheers

gmatclubot

Re: absolute value
[#permalink]
21 Mar 2006, 03:37

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