Question

show that the sum of two irrationals can be rational?

Answer 1

try
\[(1+\sqrt{2})+(1-\sqrt{2})\]

Answer 2

or
\[\sqrt{2} - \sqrt{2} = 0\]

Answer 3

In case you think a rational has to be a fraction, you can put 1/4 instead of 1 in satellite73 answer:-)