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