Question

Is the sum or product of two irrational numbers always irrational?

Answer 1

1. The sum of two irrational numbers is not necessarily irrational. For example, $\sqrt{2}\text{ and }-\sqrt{2}$ are two irrational numbers, but $\sqrt{2}+(-\sqrt{2})=0$ is rational.
2. The product of two irrational numbers is not necessarily irrational. For example $\sqrt{2}.\sqrt{2}=2$ is rational.