Question

Assertion: $\sqrt{3}$ is an irrational number.
Reason : The sum of a rational number and an irrational number is an irrational number.
Which of the following is correct?

• A. Both A and R are true and R is the correct explanation of A.
• B. Both A and R are true and R is not the correct explanation of A.
• C. A is true and R is false.
• D. A is false and R is true.

Answer 1

The correct option is B

Both A and R are true and R is not the correct explanation of A.

Assertion: $\sqrt{3}$ is an irrational number.

An irrational number is a number that can't be written in the form $\frac{p}{q},p$and $q$ are integer and $q\ne 0$.

$\sqrt{3}$ given in the assertion follows the above condition.

Therefore Assertion is true.

Reason: The sum of a rational number and an irrational number is an irrational number.

For example, let $2$ be the rational and $\sqrt{6}$ be the irrational number.

Addition of $2$ and $\sqrt{6}$ is

$2+\sqrt{6}=2+2.44948...=4.44948...$(irrational number) [$\sqrt{6}=2.44948...$ is used ]

Hence, Reason is true.

But the Reason is not the correct explanation for Assertion because there is nothing related to sum of a rational number and an irrational number in Assertion.

Hence, option B is correct.