Thread: When is the sum of 2 irrational numbers irrational?

I know that the sum of 2 irrational numbers is not always irrational (eg ), but do there exist conditions on 2 irrational numbers such that if they hold then their sum is also irrational?

Originally Posted by r45

I know that the sum of 2 irrational numbers is not always irrational (eg ), 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. ) ??