Are there two irrational numbers whose sum and product both are rational? Justify.

(N/A) Yes,there exist such irrational numbers.
Consider two irrational numbers $a = 3 + \sqrt{2}$ and $b = 3 - \sqrt{2}$.
Sum: $(3 + \sqrt{2}) + (3 - \sqrt{2}) = 6$,which is a rational number.
Product: $(3 + \sqrt{2}) \times (3 - \sqrt{2}) = (3)^2 - (\sqrt{2})^2 = 9 - 2 = 7$,which is also a rational number.
Thus,$3 + \sqrt{2}$ and $3 - \sqrt{2}$ are two irrational numbers whose sum and product are both rational.