Question

Which of the following is a correct statement?
(a) Sum of two irrational numbers is always irrational
(b) Sum of a rational and irrational number is always an irrational number
(c) Square of an irrational number is always a rational number
(d) Sum of two rational numbers can never be an integer

Answer 1

The sum of irrational number and rational number is always irrational number.

Let a be a rational number and b be an irrational number.

Then,

As 2ab is irrational therefore is irrational.

Hence is irrational.

Therefore answer is .