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Important question on roots and exponents

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Important question on roots and exponents [#permalink] New post 02 Nov 2009, 10:52
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, 13:17
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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, 21:23
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, 17:54
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, 20:27
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, 21:07
check this link http://www.mathpath.org/concepts/princi ... 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, 21:07
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