Question

If we take the sum of an irrational number and a rational number, resulting sum is always irrational.

• A. may be natural
• B. may be irrational

Answer 1

The correct option is A

may be natural

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.