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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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if x <0 then |x| = -x so this way we get \(\sqrt{(-x)*(-x)}\) i.e. \(\sqrt{x^2}\) i.e. |x|. As already said, |x| = -x, Option A is correct.
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\(\sqrt{-x^2}\) is NOT CORRECT. lets say x=-2. put this value in \(\sqrt{- (-x)*(-x)}\) and you get \(\sqrt{- (-(-2))*(-(-2))}\) i.e. \(\sqrt{- (2)*(2)}\) i.e. \(\sqrt{- 4}\) , which is not defined.

\(\sqrt{(-x)*(-x)}\) is correct. because x is negative and in this case first of all, you just place |x| in terms of x and i.e -x. Multuply -x with itself will give x^2. now square root of x^2 is nothing but |x| which is -x in our case.
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if x <0 then |x| = -x so this way we get \(\sqrt{(-x)*(-x)}\) i.e. \(\sqrt{x^2}\) i.e. |x|. As already said, |x| = -x, Option A is correct.

This is incorrect. If x < 0, then we get \(\sqrt{- (-x)*(-x)}\) i.e. \(\sqrt{-x^2}\)

HKD1710 has already provided a good explanation but you need to realize that when you assume x<0 , only the |x| portion of the expression \(\sqrt{(-x)*|x|}\) will change to \(\sqrt{(-x)*(-x)}\) and NOT \(\sqrt{- (-x)*(-x)}\)

You are writing x as -x as well which is NOT correct, giving you an extra -1 than what is should be. 'x' will remain as such.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Nice work whiplash! I agree 100% that plugging in numbers is often the most efficient (and least susceptible to careless errors) method on this kind of problem. One addt'l tip--it can be a timesaver to avoid 0, 1 (& -1), and numbers in the answer choices on a problem solving question (as opposed to on data sufficiency question, when you actually WANT to find the exceptions to the rule) because those are special numbers with special properties (the result of squaring 0 and 1 is the same as the number you put in, which is unusual) . Notice that the result of plugging in -1 is 1, which is choice A but it is *also* choice C. If you start with a small prime number like 2 or 3 (or in this case 2's negative relative, -2) you can sometimes save yourself a second pass.

hi

please comment on below...?

√- x^2

if the square root over and the square get cancelled out, we are left with "-x"

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