Sum of an irrational number and a rational number is always irrational. Take for example 1/2 + [tex]\pi [/tex]. Clearly, 1/2 is rational and its decimal expansion is equal to 0.5, while [tex] \pi [/tex] is irrational and has a non-repeating, non-terminating decimal expansion. When you add the two, you are obviously going to get a non-repeating, non-terminating decimal expansion, hence the sum is irrational.
