Question

Which of the following is a correct statement?

विकल्प

•  Sum of two irrational numbers is always irrational

• Sum of a rational and irrational number is always an irrational number

• Square of an irrational number is always a rational number

• 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,

`(a + b)^2 = a^2 +b^2 + 2ab`

                 `= (a^2 + B^2) +2ab`

As 2ab is irrational therefore  `(a + b)^2` is irrational.

Hence (a + b) is irrational.