Question

Assertion (A): \(\sqrt{10}\) is an irrational number.

Reason (R): If m is a natural number which is not a perfect square then \(\sqrt{m}\) 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 10 is a natural number that is not a perfect square, \(\sqrt{10}\) is irrational.

Step 2 – Reason: R is true. It states that the square root of a natural number that is not a perfect square is irrational.

Step 3 – Link: Applying this fact to 10 directly establishes that \(\sqrt{10}\) is irrational, so R correctly explains A.