Question

Assertion(A): `(2 + sqrt3)sqrt3` is an irrational number.

Reason(R): Product of two irrational numbers is always irrational.

Options

• Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

• Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).

• Assertion (A) is true but reason (R) is false.

• Assertion (A) is false but reason (R) is true.

Answer 1

Assertion (A) is true but reason (R) is false.

Explanation:

 While `(2 + sqrt3)sqrt3` = `2  sqrt3  + sqrt3` is irrational, the reason (R) is false because the product of two irrational numbers can sometimes be rational, e.g., `(sqrt2 xx sqrt2 = 2)`.