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

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

I know that the sum of 2 irrational numbers is not always irrational (eg $\displaystyle (1 + \sqrt{2}) + (1 - \sqrt{2}) = 2$), but do there exist conditions on 2 irrational numbers such that if they hold then their sum is also irrational?

2. Originally Posted by r45
I know that the sum of 2 irrational numbers is not always irrational (eg $\displaystyle (1 + \sqrt{2}) + (1 - \sqrt{2}) = 2$), 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. $\displaystyle \sqrt{2} + 6\sqrt{2} = 7\sqrt{2}$) ??