Question

give an example of two different irrational numbers who sum is an irrational number ,product is an irrational number

Answer 1

$\sqrt{6 } + \sqrt{2} = \sqrt{6} + \sqrt{2} \\ \\ \sqrt{6} \times \sqrt{2} = \sqrt{12}$

Answer 2

Normally, sum of any two irrational numbers is an irrational number. However, consider √2 and -√2. Their product is -2 and sum is 0, both of which are rational numbers.