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Important question on roots and exponents

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benjiboo
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Important question on roots and exponents [#permalink] New post   02 Nov 2009, 11:52
On the GMAT we are told by the GMAC that: the value of \(4^2\) has two values, +2 and -2. However the value of Square root of 4 has only one value, 2.

However, 4^1/2 equals square root 4. So my problem is, when you translate between fractional exponents and roots, what happens with the rule?

If the GMAT write down 4^1/2, does that mean if I translate it to square root 4 I only have 1 answer? Because 4^1/2 sorta has two answers. Or is it that you always need to translate 4^1/2 into square root 4 because its not proper to have fractional exponents?

Someone help, thanks :)



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Re: Important question on roots and exponents [#permalink] New post   02 Nov 2009, 14:17
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On the GMAT you are only tested about the positive results of square root operations, so \(\sqrt{4}\) has only one solution - 2

This does make things a bit funny, and most don't even think/know about this. However, it is a wall for mathematically inclined to climb over :)
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Re: Important question on roots and exponents [#permalink] New post   02 Nov 2009, 22:23
benjiboo wrote:
On the GMAT we are told by the GMAC that: the value of \(4^2\) has two values, +2 and -2. However the value of Square root of 4 has only one value, 2.

However, 4^1/2 equals square root 4. So my problem is, when you translate between fractional exponents and roots, what happens with the rule?

If the GMAT write down 4^1/2, does that mean if I translate it to square root 4 I only have 1 answer? Because 4^1/2 sorta has two answers. Or is it that you always need to translate 4^1/2 into square root 4 because its not proper to have fractional exponents?

Someone help, thanks :)


\(4^2\) (4^2) has only one value: 16

I think you mean \(\sqrt{4}\) :wink:
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Re: Important question on roots and exponents [#permalink] New post   06 Nov 2009, 18:54
Here is my problem:

\(X^2\) has two solutions, one positive and one negative.

|X| has two solutions, one positive and one negative

\(\sqrt{X^2}\) = |X|

However, GMAT states that \(\sqrt{X}\) has only one solution, the positive value.

SO...

\(\sqrt{25}\) = 5

but according to the GMAT

\(\sqrt{5^2}\) = 5 and -5

yet 25 = \(5^2\)

I am confused! Help?
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Re: Important question on roots and exponents [#permalink] New post   06 Nov 2009, 21:27
I am confused too now. So according to GMAT \(\sqrt{x}\) has only positive value?????
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Re: Important question on roots and exponents [#permalink] New post   06 Nov 2009, 22:07
check this link https://www.mathpath.org/concepts/princ ... e.root.htm

it talk about principal square root, is that it for GMAT too, GMAT considers only principal square root?



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Re: Important question on roots and exponents [#permalink]
06 Nov 2009, 22:07
Moderator:
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