# Which of the following is a correct statement?

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

Solution:

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

Let be a rational number and be an irrational number.

Then,

$(a+b)^{2}=a^{2}+b^{2}+2 a b$

$=\left(a^{2}+b^{2}\right)+2 a b$

As $2 a b$ is irrational therefore $(a+b)^{2}$ is irrational.

Hence $(a+b)$ is irrational.

Therefore answer is $b$.