# Which of the Following is a Correct Statement? - Mathematics

MCQ

Which of the following is a correct statement?

#### Options

•  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

#### Solution

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.

Concept: Concept of Irrational Numbers
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 1 Number Systems
Exercise 1.7 | Q 3 | Page 40

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