Give an example of two irrational numbers whose sum as well as the product is rational.
Let two irrational numbers be 10 + 2√5 and 5 - 2√5
(i) sum is rational
= 10 + 2√5 + 5 - 2√5
= 15 (a rational number)
(ii) product is rational are
= (10 + 2√5) (10 - 2√5)
= (10)2 - (2√5)2
= 100 - 20 = 80 (a rational number)