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August 31st, 2017, 06:22 PM   #1
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Positive or negative root

Hey,
Just a quick question for advice on how you all remember to do this.
Take the example:
V^2=4
V=+\-square root(4)
Excuse the lack of symbols, pretty new to posting online.

I always forget to include the plus or minus sign before the square root.
Does anyone have a quick mental way to remember, or will it come naturally.
Thanks from verygoodatmaths
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August 31st, 2017, 06:28 PM   #2
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You need to be more careful. Focus on exactly what it is you are doing and think of all possible ways of doing it. Don't feel bad - I have had (and still have, at times) an annoying carelessness - we all do from time to time.

Learning by rote may be helpful - do several problems involving squared quantities.
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August 31st, 2017, 06:29 PM   #3
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I think you just need to understand why square root(x) = +/-x^2.

For example, if we take root(4), we need to find what value(s), when squared, equal 4.
2^2 = 2 x 2 =4
(-2)^2 = -2 x -2 =4

Hence, root(4) = +/-2

Hope I helped
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September 1st, 2017, 07:20 AM   #4
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Just to add to this, when we write $\sqrt{a}$ (where $a$ is a non-negative real number), we are referring specifically to the non-negative root. The key point is that if you are told $x^2 = a$, this does not imply that $x = \sqrt{a}$ - it implies that $x = \sqrt{a}$ or $x = -\sqrt{a}$.
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