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

Answer 1

The correct option is C

is always rational

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