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    Integral Domains, Fields and Subfields

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    Problem:
    Note: Q is rational numbers, R is real numbers ,
    sqrt() means square root

    Show that Q(sqrt(2)) is the smallest subfield of R that contains sqrt(2).

    © BrainMass Inc. brainmass.com March 4, 2021, 5:54 pm ad1c9bdddf
    https://brainmass.com/math/integrals/integral-domains-fields-subfields-17276

    Solution Preview

    Proof:
    First, Q(sqrt(2)) is a subfield of R. An arbitrary element in Q(sqrt(2)) has the form x=a+bsqrt(2) with a,b in Q. We note ...

    Solution Summary

    A proof involving rational and real numbers is provided.

    $2.49

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