Write a pair of irrational numbers whose product is rational.

Let $5 + \sqrt{2} \text{ and } 5 - \sqrt{2}$ be two irrational numbers.

Product of numbers

$= (5 + \sqrt{2})(5 - \sqrt{2}) \\[1em] = 25 - 5\sqrt{2} + 5\sqrt{2} - 2 \\[1em] = 23.$

23 is a rational number.

Hence, required pair = $5 + \sqrt{2} \text{ and } 5 - \sqrt{2}$.