well the whole thing is a square root ( STEM^1/2 )

and remember we can only have POSITIVE roots from a square root

abs(x) = - x if x< 0
abs(x)= + X if X>0

Since we have a MINUS sign in the expression, X can not be > 0

because ;

(-x^2) ^1/2 is not a real number

so the inside of the expression should look like

(x^2) which means that abs(x) needs to be -X

So A is correct

sushanta57021 wrote:[-X{abs(X)}]^1/2

A. -x
B. x
C. 1
D. -1
E. x^1/2

the answer is A.
can some one please explain?

Thanks.[/img]

[/quote]

How about we make life simple and just pick x=-4 and sub in.

(Note that i'm picking a negative number because otherwise we'll end up taking the root of a negative, which doesn't work out so well!)

[-X{abs(X)}]^1/2
[4(4)]^1/2
(16)^1/2
4

When we plug in -4 to the choices, only (a) gives us "4": choose (a).

[/quote]
How about we make life simple and just pick x=-4 and sub in.

(Note that i'm picking a negative number because otherwise we'll end up taking the root of a negative, which doesn't work out so well!)

[-X{abs(X)}]^1/2
[4(4)]^1/2
(16)^1/2
4

When we plug in -4 to the choices, only (a) gives us "4": choose (a).[/quote]

I appreciate it.
but 16^1/2 can be -4 as well. which means the answer is +X
in my opinion the answer choices are wrong as the answer can be +X or -X.

Can you follow this thread to answer the question, but i wrongly post the question on the DS section.
https://www.beatthegmat.com/algebra-t22739.html

waiting for your reply

sushanta57021 wrote: When we plug in -4 to the choices, only (a) gives us "4": choose (a).

I appreciate it.
but 16^1/2 can be -4 as well. which means the answer is +X
in my opinion the answer choices are wrong as the answer can be +X or -X.

Can you follow this thread to answer the question, but i wrongly post the question on the DS section.
https://www.beatthegmat.com/algebra-t22739.html

waiting for your reply

16^(1/2) = +4 or - 4 YOU ARE RIGHT

BUT,

(-16)^(1/2) = Is not a real number.

SO INSIDE OF THE ROOT needs to be POSITIVE (+) , not OUTSIDE OF IT!

Clear now ?

16^(1/2) = +4 or - 4 YOU ARE RIGHT

BUT,

(-16)^(1/2) = Is not a real number.

SO INSIDE OF THE ROOT needs to be POSITIVE (+) , not OUTSIDE OF IT!

Clear now ?

-4 = {-(-4)x4}^1/2
is there any with the above eqn.
that means if X= -4, then also the above equation can be -4, that is X.
i am trying to explain it over and over, but i really did not understand what did you want to mean by the bold line above.
this is not relevant to the problem.
hope you understand it now.

sushanta57021 wrote:

16^(1/2) = +4 or - 4 YOU ARE RIGHT

BUT,

(-16)^(1/2) = Is not a real number.

SO INSIDE OF THE ROOT needs to be POSITIVE (+) , not OUTSIDE OF IT!

Clear now ?

-4 = {-(-4)x4}^1/2
is there any with the above eqn.
that means if X= -4, then also the above equation can be -4, that is X.
i am trying to explain it over and over, but i really did not understand what did you want to mean by the bold line above.
this is not relevant to the problem.
hope you understand it now.

Alright,

root of a negative number is called imaginary number.

https://en.wikipedia.org/wiki/Imaginary_number

You can also call it NOT REAL.

Alright,

root of a negative number is called imaginary number.

https://en.wikipedia.org/wiki/Imaginary_number

You can also call it NOT REAL.

Thanks for your info. But i think i know the definition of imaginary no.
What i wanted to mean was, this info is irreverent to the problem.

the question started with X<0,

I don't know whether your understood my concern clearly;
but your explanation for the problem is not towards that direction

One more time:

[-X{abs(X)}]^1/2

A. -x
B. x

Lets solve this equation for both -x and + x

-X

[-X{abs(X)}]^1/2

[-(-X){abs(-X)}]^1/2

[ X X ]^1/2 = X


X

[-X{abs(X)}]^1/2

[-(X){abs(X)}]^1/2

[ - X X ]^1/2 = No solution

If you still have some doubts, I have nothing to add to this explanation. Sorry

Sushanta,


If I understood you right u r saying sqrt(16) can be +4 or -4 correct.

sqrt(x) is always equal to |x| i.e absolute value of x. This is called the principal square root of x that applies to math world and GMAT.

Prinicipal square root of a number is the unique nonnegative square root of a nonnegative real number. For example, the principal square root of 16 is 4 , although both 4 and -4 are square roots of 16

For positive real number R (16 FOR EG) when we say square root of R we refer to the psotive sqaure root of R


Referring to the actual GMAT PREP question:

Taking in to account what I said above if you take x=-4 like Stuart explained you will get +4 as the square root which is -x (since x=-4 and -(-4) = 4 which you already know)

Let us know if u still have questions!

Regards,
Cramya

cramya wrote:Sushanta,


If I understood you right u r saying sqrt(16) can be +4 or -4 correct.

sqrt(x) is always equal to |x| i.e absolute value of x. This is called the principal square root of x that applies to math world and GMAT.

Prinicipal square root of a number is the unique nonnegative square root of a nonnegative real number. For example, the principal square root of 16 is 4 , although both 4 and -4 are square roots of 16

For positive real number R (16 FOR EG) when we say square root of R we refer to the psotive sqaure root of R


Referring to the actual GMAT PREP question:

Taking in to account what I said above if you take x=-4 like Stuart explained you will get +4 as the square root which is -x (since x=-4 and -(-4) = 4 which you already know)

Let us know if u still have questions!

Regards,
Cramya

I appreciate that, atleast you are trying to explain it in the proper direction.
as per your explanation 16^1/2 =4.
this is fine, but does not mean 16^1/2 = -4 is wrong, specially when a separate answer choice explicitly mentions about this option, then we can not completely discard it.
So I strongly believe the options are not right in that question.

But anyway, we had enough discussion on that question. there's nothing more to add really, as Logitech rightly mentioned.

anyway thanks everybody......

appreciate that, atleast you are trying to explain it in the proper direction.
as per your explanation 16^1/2 =4.
this is fine, but does not mean 16^1/2 = -4 is wrong, specially when a separate answer choice explicitly mentions about this option, then we can not completely discard it.
So I strongly believe the options are not right in that question

No Problem! Its not wrong but the key is in recognizing whats accepted /endorsed in the Math World and GMAT when the y say square root of a number as I mentioned in my previous post. They specically put x as that was the trap answer.

Not to repeat myself but the key is knowing For positive real number R (16 FOR EG) when we say square root of R we refer to the psotive sqaure root of R This is the norm or whats accepeted that I was talking about before


Refer to (outside of scope of what we need to know for GMAT really but if its helps you any)

https://www.mathpath.org/concepts/princi ... e.root.htm

It provides a nice explanation on what I mentioned rather briefly.