## Calculus: Early Transcendentals 8th Edition

(a) The sum of two irrational numbers is not always an irrational number. Consider the below two irrational numbers $2+\sqrt 3,2-\sqrt 3$. Their sum is 4 which is not an irrational number. Hence, the sum of two irrational numbers is always not an irrational number. (b) The product of two irrational numbers is always not an irrational number. Consider the below two irrational numbers $2+\sqrt 3,2-\sqrt 3$. Their product is 1 which is not an irrational number. Hence, the product of two irrational numbers is not always an irrational number.