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    Find Irreducible Polynomial

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    Find an irreducible polynomial defining the extension Q(3^1/2, 5^1/2).

    © BrainMass Inc. brainmass.com December 24, 2021, 4:51 pm ad1c9bdddf


    Solution Preview

    Let K=Q(sqrt(3),sqrt(5))
    Degree of K:Q=4
    Let a=sqrt(3)+sqrt(5) (1),

    THEN we'll prove that K=Q(a)

    We have:a^2= 8+2*sqrt(15)
    a^4= 124+ 32*sqrt(15)=16*a^2-4 (from ...

    Solution Summary

    An irreducible polynomial defining an extension is found.