Question

When a rational and an irrational number are added, is the sum rational or irrational? Explain.

Answer 1

Sum of an irrational number and a rational number is always irrational. Take for example 1/2 + $\pi$. Clearly, 1/2 is rational and its decimal expansion is equal to 0.5, while $\pi$ 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.