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Math Help - When is the sum of 2 irrational numbers irrational?

  1. #1
    r45
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    When is the sum of 2 irrational numbers irrational?

    I know that the sum of 2 irrational numbers is not always irrational (eg (1 + \sqrt{2}) + (1 - \sqrt{2}) = 2), but do there exist conditions on 2 irrational numbers such that if they hold then their sum is also irrational?
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    Member pflo's Avatar
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    Quote Originally Posted by r45 View Post
    I know that the sum of 2 irrational numbers is not always irrational (eg (1 + \sqrt{2}) + (1 - \sqrt{2}) = 2), but do there exist conditions on 2 irrational numbers such that if they hold then their sum is also irrational?
    I don't have much experience with this sort of thing and I'm not willing ot put in a bunch of time proving an algorithm, but here's one scenario I thought of: If one is a multiple of the other (e.g. \sqrt{2} + 6\sqrt{2} = 7\sqrt{2}) ??
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