# Which of the following statements is false?

## The sum of two rational numbers is always rational. The sum of a rational number and an irrational number is always rational. The product of a nonzero rational number and an irrational number is always irrational. The product of two irrational numbers is either rational or irrational.

Jun 7, 2017

For example, take $\sqrt{2} + 1$, we don't know what $\sqrt{2}$ is, so we can't know what $1$ more than it is.