Question

Assertion (A): `(a + sqrt(b)) · (a - sqrt(b))` is a rational number, where a and b are positive integers.

Reason (R): Product of two irrationals is always rational.

Options

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

• Both Assertion (A) and Reason (R) are true, but Reason (R) is not correct explanation for 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:

`(a + sqrt(b))(a - sqrt(b))`

= `a^2 - (sqrt(b))^2`

= a² – b, which is a rational number.

So, Assertion is true.

Hence, the product of two irrationals may be rational or irrational.

So, Reason is false.