Question

Assertion: `3/(sqrt(6) + sqrt(3)) = sqrt(6) - sqrt(3)`

Reason: The rationalising factor of `sqrt(6) + sqrt(3)` is `sqrt(6) - sqrt(3)`.

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

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

Explanation:

Let’s analyse the assertion and reason:

Assertion: 

To verify this assertion, multiply the numerator and denominator by the conjugate of the denominator:

`3/(sqrt(6) + sqrt(3)) xx (sqrt(6) - sqrt(3))/(sqrt(6) - sqrt(3))`

= `(3(sqrt(6) - sqrt(3)))/(sqrt(6)^2 - (sqrt(3))^2`

= `(3(sqrt(6) - sqrt(3)))/(6 - 3)`

= `(3(sqrt(6) - sqrt(3)))/3`

= `sqrt(6) - sqrt(3)`

Thus, the assertion is true.

Reason:

By definition, the rationalising factor of an expression (a + b) with square roots is its conjugate (a – b), used to eliminate the surds in the denominator by multiplying the numerator and denominator by this conjugate.

Here, the rationalising factor of `sqrt(6) + sqrt(3)` is indeed `sqrt(6) - sqrt(3)`, so the reason is correct.

Since both assertion and reason are true and reason correctly explains the assertion.