Question

If we take the sum of an irrational number and a rational number, which of the following options hold true regarding the resulting sum?

• A. It may be natural.
• B. It may be irrational.
• C. It is always rational.
• D. It is always irrational.

Answer 1

The correct option is D

It is always irrational.

The decimal representation of an irrational number is non-terminating non-recurring and the decimal representation of a rational number is either terminating or non-terminating recurring. Adding both of them, we always get a non-terminating, non-recurring decimal. Hence it is always irrational.