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If x<0, then root(-x*|x|) is:

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Senior Manager
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Joined: 24 Mar 2015
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Re: If x<0, then root(-x*|x|) is:  [#permalink]

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06 Aug 2017, 07:35
parker wrote:
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

√- x^2

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

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If x<0, then root(-x*|x|) is:  [#permalink]

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06 Aug 2017, 09:02
I am not sure if my solution makes sense, but that's how I get it into my mind(negative values under the square root)

\sqrt{−x∗|x|} = -(x*|x|)^1/2= -(x^2)^1/2 = - (x) = -x
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Re: If x<0, then root(-x*|x|) is:  [#permalink]

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22 Nov 2017, 13:30
nss123 wrote:
If x<0, then $$\sqrt{-x|x|}$$ is:

A. -x
B. -1
C. 1
D. x
E. $$\sqrt{x}$$

Since x is less than zero, |x| = -x.

Thus, we have:

√(-x|x|) = √(-x(-x)) = √(x^2)

Recall that √(x^2) = |x|; however, |x| = -x, since x is less than zero, so we have:

√(-x|x|) = √(-x(-x)) = √(x^2) = |x| = -x

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If x<0, then root(-x*|x|) is:  [#permalink]

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22 Nov 2017, 18:09
1
cbh wrote:
I am not sure if my solution makes sense, but that's how I get it into my mind(negative values under the square root)

\sqrt{−x∗|x|} = -(x*|x|)^1/2= -(x^2)^1/2 = - (x) = -x

cbh and gmatcracker2018, read, above, from this post down tothis post. Your issue is discussed.

And to both . . .If you want comments, I think you will have better luck if you format properly. Speaking of, I think you both mean:

$$\sqrt{−x∗|x|}=$$

$$\sqrt{-(x*|x|)} =$$

$$\sqrt{-(x^2)} =$$

$$- (x) = -x$$

When it is written like that, does it look strange?
Any number squared is positive or 0 (non-negative). Full stop.

When was the last time you took the square root of a negative number? The people above articulate additional issues more eloquently than I can.

I learned to plug in an actual negative number in these kinds of questions. I recommend it.

santro789 , the negative of a negative is a positive. Change the parentheses, to emphasize "opposite of":
(-)-3 = 3

If $$x<0$$, then $$|x|= -x$$. This concept can be counterintuitive.

I listed a few ways of thinking about it here.

Then Bunuel added even more ways to think about it just after that, here.

Hope that helps.
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Re: If x<0, then root(-x*|x|) is:  [#permalink]

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24 Nov 2018, 10:08
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Re: If x<0, then root(-x*|x|) is:   [#permalink] 24 Nov 2018, 10:08

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