if x<0, then sqrt(-x|x|) is

[2amitprakash]

if x<0, then sqrt(-x|x|) is
A. -x
B. -1
C. 1
D. x
E. sqrt(x)

I'm confused for the answer choices A & D. For me both A and D are true.
Solution:
x < 0, so |x| = -x
hence sqrt (-x|x|) is sqrt (x2) which has 2 solutions x and -x.


OA: A (highlight to see it)

[nitin_prakash_khanna]

The quick way to approach will be pick a number x<0

Lets pick -5

so we know x=-5

sqrt (-x|x|) = sqrt (-(-5)|-5|)
= sqrt (5*5) = sqrt (25) = 5 = -(-5) = -x

So Answer A.

[2amitprakash]

Thanks nitin! But your explanation also has the same issue which I have in my solution. What if I consider sqrt(25) = -5?

However while analysing your solution, I think I got my answer.

The correct solution for sqrt(x2) can be thought of as |x| and then the puzzles fit in.

[RonPurewal]

Thanks nitin! But your explanation also has the same issue which I have in my solution. What if I consider sqrt(25) = -5?

you can't consider that, because that's wrong.

the "√" symbol (i.e., the thing you're writing as "sqrt") is ALWAYS non-negative. that is how it's defined.

The correct solution for sqrt(x2) can be thought of as |x| and then the puzzles fit in.

this is correct. it's not just "thought of" as |x|; it actually IS |x|.
...because |x| is always non-negative. this fits the definition of "√" precisely.

[2amitprakash]

The correct solution for sqrt(x2) can be thought of as |x| and then the puzzles fit in.

this is correct. it's not just "thought of" as |x|; it actually IS |x|.
...because |x| is always non-negative. this fits the definition of "√" precisely.

Thanks, Ron! I'll now remember this as "IS". I never thought of √x2 as |x| although using so always:).

[agha79]

= sqrt (5*5) = sqrt (25) = 5 = -(-5) = -x

Hi nitin_prakash_khanna -

I am having trouble understanding the last part. when we sqrt (25) = 5 but why than we are saying -(-5) = -x

[nitin_prakash_khanna]

Hi "agha79"

two things, i hope you understood Ron's post where he mentioned √x2 = |x|
i.e √25 = 5 only not -5.

Now if you got that then
5 can be written as - (-5) , -1 * -1 = +1

And we picked x =-5 intially as our plug in so
- (-5) = -x , which is the answer.

Hope it helps.

[MBA-Bound]

I am confused on the last part. If x is a negative then the absolute value is positive. The logic below seems wrong, because -(-5) should be a positive. Where does the -x come from?

And we picked x =-5 intially as our plug in so
- (-5) = -x , which is the answer.

[nitin_prakash_khanna]

all right folks let me attempt to explain

The question says x<0

and asks us to find √(-x*|x| = ?

since x is negative we picked x = -5 just to satisfy the question stem requirement.

So far so good?

next lets calculate the value of √(-x*|x|) = √(-(-5) * |-5| = √5*5 = √25

i am assuming we dont have any dispute till this point.

next the is conceptual thing.....we realize that √ sign represents the positive square root .

so √25 = 5.

so our expression √(-x*|x|) comes out to be 5 when we picked x=-5.

which is negative of x so

√(-x*|x|) = -x

Does this sound ok. Only thing is we were trying to reresent 5 as negative of negative 5 i.e -(-5) , so that we can see our original plug in value of -5, but anyways that point is irrelevant if you got the above stuff.

[kannan_m_80]

this is a tricky one, and can be solved easily if we plug in numbers..thanks nitin

[RonPurewal]

I am confused on the last part. If x is a negative then the absolute value is positive. The logic below seems wrong, because -(-5) should be a positive. Where does the -x come from?

(-x) is a positive quantity, since x is negative.

[maddy2u]

Why shouldn't the value of x be negative. It will still be correct !!

[RonPurewal]

Why shouldn't the value of x be negative. It will still be correct !!

not quite sure what you're asking here -- please explain in more detail, thanks

the problem actually specifies, explicitly, that x < 0; therefore, it's a given that x is negative. given this fact, it's difficult to understand exactly what you are asking here.

[AmunaGmat]

if x<0, then sqrt(-x|x|) is
A. -x
B. -1
C. 1
D. x
E. sqrt(x)

I'm confused for the answer choices A & D. For me both A and D are true.
Solution:
x < 0, so |x| = -x
hence sqrt (-x|x|) is sqrt (x2) which has 2 solutions x and -x.


OA: A (highlight to see it)

Although there are explanations to this questions, I am still stuck at +/- X as the value of the sqrt. I do not get why or how we drop the positive part of the solution. Ron can you please help?

[jnelson0612]

if x<0, then sqrt(-x|x|) is
A. -x
B. -1
C. 1
D. x
E. sqrt(x)

I'm confused for the answer choices A & D. For me both A and D are true.
Solution:
x < 0, so |x| = -x
hence sqrt (-x|x|) is sqrt (x2) which has 2 solutions x and -x.


OA: A (highlight to see it)

Although there are explanations to this questions, I am still stuck at +/- X as the value of the sqrt. I do not get why or how we drop the positive part of the solution. Ron can you please help?

Please go back and read nitin's post of 10/28. You'll see that he plugs in the number -5 as x. When he plugs that in all the way through the problem, he eventually finds that he is taking the square root of 25. I ONLY obtain a positive value when I take the square root of a number. Thus, the target answer to the problem is 5 given that x=-5.

Now, I take x=-5 and plug it into the answer choices. Which one gives us 5? Answer choice A, -x. Why? Because -(-5) equals 5, which is our target answer.