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Possible Duplicate:
$a^{1/2}$ is either an integer or an irrational number.

Will every $n^{th}$ root of $2$ be an irrational number? If yes, how can I prove that?

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    http://math.stackexchange.com/questions/4467/a1-2-is-either-an-integer-or-an-irrational-number2010-11-25
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    Hint: Fermat's last theorem comes to mind when you want to prove it for n>2. Then proof it for n=2 and you got it.2010-11-25
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    In fact $n^{th}$ root of a number, which is not a perfect $n^{th}$ power of an integer, will always be an irrational number.2010-11-26
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    @Max: pretty much the worst way to do this problem...2010-11-26
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    @Qiaochu: I believe there was a mention of that in the "mosquito-nuking" thread in MO...2010-11-26
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    @J.M.: I think FLT for this problem is not "mosquito-nuking" but "bacteria-nuking"2010-11-26
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    I think that the most important thing is that the mosquito, bacteria or whatever is dead because of the FLT-nuke.2010-11-26
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    @J.M. I rolled back your tag edit (as I did another of your recent edits). Please be careful editing tags in fields for which you may not have expert knowledge.2012-01-03
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    Look, @Bill, we're trying to eradicate an exceedingly ambiguous tag here... I can see why you'd add [tag:abstract-algebra], but your removal of [tag:algebra-precalculus] sounds iffy to me. But hey, you're the "expert", good sir.2012-01-03
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    Why are people fighting over the tags of a closed question?2012-01-03
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    See also http://math.stackexchange.com/questions/783028/how-would-you-prove-that-sqrtn2-is-irrational and http://math.stackexchange.com/questions/1191176/irrationality-of-sqrtn22015-10-18
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    I'm late, but I was just thinking about this.2018-11-28

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