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