Where an I wrong?

[umaa]

If x<0, then sqrroot(-x|x|) is,

A. -x
B. -1
C. 1
D. 0
E. x

Ans is, A

My answer is E

[Neo2000]

If X is less than Zero, then Mod of x = -x

Your question now becomes sqrt(-x(-x)) = sqrt(x^2) = Plus or Minus X

Again since X is less than Zero, your answer becomes Minus X

[umaa]

But there is no + or - for sqrroot right? We normally take sqrroot of 4 as 2. Are we taking it as + or - 2?

[Neo2000]

Strictly speaking,

Every positive number x has two square roots. One of them is +\sqrt{x}, which is positive, and the other -\sqrt{x}, which is negative. Together, these two roots are denoted Plus or Minus\sqrt{x}

[umaa]

Got it. Thx.

[aroon7]

Strictly speaking,

Every positive number x has two square roots. One of them is +\sqrt{x}, which is positive, and the other -\sqrt{x}, which is negative. Together, these two roots are denoted Plus or Minus\sqrt{x}

Sorry Neo! atleast in GMAT prespective this is wrong
sqrt(9) is 3 is what OG11 says (pg 114 under Powers and roots of numbers)
"...sqrt(n) denotes positive number whose square is n"
only when x^2 = 9, x = 3 or -3

[aroon7]

sorry forgot to justify option A

sqrt(-x|x|) will give us absolute value of x. since x is already negative -x is positive.

eg: x = -2
sqrt(2*2) = 2 = -(-2) = -x

[Ian Stewart]

Strictly speaking,

Every positive number x has two square roots. One of them is +\sqrt{x}, which is positive, and the other -\sqrt{x}, which is negative. Together, these two roots are denoted Plus or Minus\sqrt{x}

Sorry Neo! atleast in GMAT prespective this is wrong
sqrt(9) is 3 is what OG11 says (pg 114 under Powers and roots of numbers)
"...sqrt(n) denotes positive number whose square is n"
only when x^2 = 9, x = 3 or -3

aroon - you say that Neo is wrong, and then go on to agree with everything he said! You're both right, of course. First, math on the GMAT is just like math anywhere else - there is no 'GMAT perspective' on math that is any different from the perspective in your high school math class (I suppose with one exception - the GMAT does not include complex numbers). Second, as Neo points out above, and as the OG says (pg. 114, middle of the page), "Every positive number n has two square roots, one positive, and the other negative, but *sqrt(n)* denotes the positive number whose square is n." That is, 9 has two square roots, 3 and -3, because 3^2 = 9 and (-3)^2 = 9. However, the square root symbol is defined so that it only gives us the positive square root, if there is a positive number under the root. So if you see sqrt(9), by which I mean: "9 underneath the square root symbol", that only has one answer: 3. If, however, I say, in words, "x is a square root of 9", then there are two possible values for x, 3 and -3.

[yvichman]

what do you mean by Mod of X?

[aroon7]

I agree with you Ian. But, when there is a root sign already then we shouldnot include a + or - before it... that is what i wanted to say

what do you mean by Mod of X?

mod of X is the absolute value of X. it is defined as the distance from 0 to point X on the number line
mod (2) = mod (-2) = 2, since are both 2 units away from 0 on a number line