Question

Give an example of each, two irrational numbers, whose product is an irrational number?

Answer 1

e is an irrational number and Π is an irrational number it's product is also

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.

Thus, there can be numbers whose sum and product both are rationals.

Hope it helps.