Which of the following statements are true regarding the sum of rational and irrational numbers? Select three that apply.

Question

A.
The sum of 0 and a rational number is an irrational number.

B.
The sum of 0 and an irrational number is an irrational number.

C.
The sum of any two nonzero rational numbers is a rational number.

D.
The sum of a nonzero rational number and an irrational number is an irrational number.

Answer 1

The true statements regarding the sum of rational and irrational numbers are:

B. The sum of 0 and an irrational number is an irrational number.

C. The sum of any two nonzero rational numbers is a rational number.

D. The sum of a nonzero rational number and an irrational number is an irrational number.

So the correct selections are B, C, and D.

Statement A is false because the sum of 0 (which is a rational number) and a rational number is still a rational number.