Prove or disprove that the sum of two irrational numbers is irrational

Question

Prove or disprove that the sum of two irrational numbers is irrational. How do i answer this? Thanks.

Answer 1

Since $-\sqrt{2} + \sqrt{2} = 0$, so the sum of two irrationals may be rational.

Answer 2

($2+\sqrt3$)+($2- \sqrt3$) $=$ $4$ which is rational. So , the statement " sum of two irrationals is irrational" is disproved since counter example is found.

When a statement like that is given to prove or disprove, " sum of two irrationals is irrational" , it is proved if it is found to be always true and disproved if at least one counter example can be given.

In fact, sum of two irrationals can be either rational or irrational. Not necessarily irrational all the time.