Question:
Give an example of two irrational numbers whose sum as well as product is rational.
Solution:
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 $=(2+\sqrt{3})(2-\sqrt{3})=2^{2}-(\sqrt{3})^{2}=4-3=1$, which is rational