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Square roots-Maths

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acegmat29 Newbie | Next Rank: 10 Posts Default Avatar
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Square roots-Maths

Post Mon Dec 19, 2016 12:19 am
when (-1)^2 and (1)^2 both is equal to 1 then why cant (1)^1/2 cant equal to both +1 and -1.. can someone explain

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Post Thu Mar 16, 2017 8:58 pm
Rich.C@EMPOWERgmat.com wrote:
While (Root9) = +3

(RootX^2) = 4 means that X could be 4 or -4
This is hard to follow without notation, so if anyone is confused, what Rich is saying here is

√9 = 3

√x² = 4 means x² = 16 means x = ±4.

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Post Thu Mar 16, 2017 8:53 pm
It isn't just the GMAT, math in general limits square roots to nonnegative solutions.

This is a tradition that stems back to the Greeks, who didn't recognize the existence of negative numbers. Since they inaugurated (or at least popularized) the notion of square roots, we go with that.

In practical terms, this means that, as you say, x² = 1 has two solutions, but √1 only has one.

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Post Mon Dec 19, 2016 7:07 am
Hi acegmat29,

The GMAT limits square roots to the POSITIVE root only. You still have to pay careful attention to what the prompt presents though.

For example:

While (Root9) = +3

(RootX^2) = 4 means that X could be 4 or -4

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