Question

Assertion (A): \[\sqrt{5}\] is an irrational number.

Reason (R): Let p be a prime number and a be a positive integer. Then, p divides \[a^{2} \Rightarrow\] p divides a.

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 but Reason (R) is not a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. Since 5 is prime and is not a perfect square, \(\sqrt{5}\) is irrational.

Step 2 – Reason: R is true. For a prime p and positive integer a, if p divides \(a^{2}\), then p divides a.

Step 3 – Link: Although R is true and is relevant to a proof of the irrationality of \(\sqrt{5}\), it does not by itself state or establish the assertion as written. Therefore, it is not the correct explanation of A.