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Math Help - Prove that you can add and multiply elements...

  1. #1
    Junior Member
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    Prove that you can add and multiply elements...

    Let Z[sqrt(2)] be all the real numbers of the form a + b*sqrt(2) with a and b integers. Prove that you can add and multiply elements in this set and always get elements in the set.
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Addition is pretty straight forward

    Multiplication:  (a+b\sqrt2)(c+d\sqrt2) = ac+2bd+(ad+bc)\sqrt2
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