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I need to find a way of proving that the square roots of a finite set of different primes are linearly independent over the field of rationals.

I've tried to solve the problem using elementary algebra and also using the theory of field extensions, without success. To prove linear independence of two primes is easy but then my problems arise. I would be very thankful for an answer to this question.

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    I need the square roots of prime numbers2011-04-03
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    http://mathforum.org/library/drmath/view/51638.html2011-04-03
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    Also, see this: http://qchu.wordpress.com/2009/07/02/square-roots-have-no-unexpected-linear-relationships/2011-04-03
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    This also comes up in T..'s answer here: http://math.stackexchange.com/questions/6244/is-there-a-quick-proof-as-to-why-the-vector-space-of-mathbbr-over-mathbbq/6517#65172011-04-03
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    @J.M.: after Yuval's hint to the mathforum I'd like to mention, that the text of the question is 100% identical with that of the mathforum of 1996, and the fact that neither its reference was given nor anything about the existing answers there was mentioned I assume a) this is not a real question (also there was no followup interaction of "user8465") , and (see the recent meta thread on spam) b) maybe not even a real person asking but possibly an automated transfer of a somehow mathematically sounding text. Maybe that method of spam has been refined recently...2011-10-11
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    add: the meta-thread on spambots which I mentioned in the previous comment is http://meta.math.stackexchange.com/questions/30632011-10-11
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    @Gottfried The question is surely not spam - see my comments [here.](http://meta.math.stackexchange.com/questions/3063/whats-up-with-all-the-spambots/3072#3072)2011-10-11

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