That's true.
In fact, suppose that x is irrational, and y is rational. If
[tex] x+y=z [/tex]
and z is rational, then you have
[tex] x = z-y [/tex]
But [tex] z-y [/tex] is the difference of two rational numbers, and the sum/difference of rational numbers is still a rational number.
This proves that the sum of a rational and an irrational number is still irrational.
