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# Square Root = Always Positive?

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Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 432

Kudos [?]: 277 [0], given: 64

GMAT 1: 790 Q51 V49
GRE 1: 340 Q170 V170
Re: Square Root = Always Positive? [#permalink]

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08 Oct 2017, 12:42
MartinSC wrote:
Bunuel wrote:
MartinSC wrote:
I was counting on that, but what about this one:

If (x-1)^2=400, which of the following could be the value of ?
(A) 15
(B) 14
(C) –24
(D) –25
(E) –26

I thought "16" applying the "always positive" mantra, but the explanation goes as follows:

"Work the problem by taking the square root of both sides and solving for x.

Thus,

(x-1)^2=400
x-1= +/-20 (wait, I was not expecting to see the negative root!!)

So x= -19 or x=21 and
x-5=-24 or x-5=16" (which is not even an option).

Seeing that 16 was not among the choices, I could have picked (C)-24, which would have been correct, but it goes against the theory of the positive root...so I was left scratching my head.

Anyone has an idea?

Thks!

When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root. That is:

$$\sqrt{9} = 3$$, NOT +3 or -3;
$$\sqrt[4]{16} = 2$$, NOT +2 or -2;

Notice that in contrast, the equation $$x^2 = 9$$ has TWO solutions, +3 and -3. Because $$x^2 = 9$$ means that $$x =-\sqrt{9}=-3$$ or $$x=\sqrt{9}=3$$.

Thanks, but in this case the correct answer is considering the negative root because (C) -24 is the correct answer. If it considered the positive root, the correct answer would have been -16, which is not even among the choices.

Am I missing something here? This is an OG question.

Rgds,

I'm glad you raised this question. It turns out that there are two different scenarios:

$$\sqrt{9}=x$$
$$9 = x^2$$

Those are two different things on the GMAT. This post goes into the specifics: https://www.manhattanprep.com/gmat/blog ... -the-gmat/
_________________

Chelsey Cooley | Manhattan Prep Instructor | Seattle and Online

My upcoming GMAT trial classes | GMAT blog archive

Kudos [?]: 277 [0], given: 64

Re: Square Root = Always Positive?   [#permalink] 08 Oct 2017, 12:42

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# Square Root = Always Positive?

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