Question

Give an example of two irrational numbers whose sum as well as product is rational.

Answer 1

Let the two irrational numbers be $2+\sqrt{3}$ and $2-\sqrt{3}$

Sum of these irrational numbers $=2+\sqrt{3}+2-\sqrt{3}=4$, which is rational

Product of these irrational numbers $=(2+\sqrt{3})(2-\sqrt{3})=4-3=1$, which is rational