Saturday, December 2, 2017

abstract algebra - The square roots of different primes are linearly independent over the field of rationals


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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