Irrational numbers are numbers that can not be written as a ratio of two integers. (example: square root of 2). Rational numbers on the other hand can be written as a ratio, as decimal or percentage.
If X is a irrational number, than the number Y=1-X is also irrational and the sum of these two irrational numbers is: X+Y=X+1-X=1 is rational number.
So, the sum of two irrational numbers can be a rational number.