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 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?