Question

Assertion (A): \[\sqrt{7}\] is an irrational number.

Reason (R): If p is prime then \[\sqrt{p}\] is irrational.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. Since 7 is prime, \(\sqrt{7}\) is irrational.

Step 2 – Reason: R is true. The square root of a prime number is irrational.

Step 3 – Link: Applying the stated result to the prime number 7 proves A, so R correctly explains it.