Question

Assertion: `1/(3 + sqrt(8)) = 3 - sqrt(8)`

Reason: (a + b)(a – b) = a² – b²

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Assertion:

`1/(3 + sqrt(8)) = 3 - sqrt(8)` (Is this true?)

Let’s rationalise the denominator of `1/(3 + sqrt(8))`:

Multiply numerator and denominator by the conjugate `(3 - sqrt(8))`:

`1/(3 + sqrt(8)) * (3 - sqrt(8))/(3 - sqrt(8)) = (3 - sqrt(8))/((3 + sqrt(8))(3 - sqrt(8))`

Use identity (a + b)(a – b) = a² – b²:

= `(3 - sqrt(8))/(9 - 8)`

= `(3 - sqrt(8))/1`

= `3 - sqrt(8)`

So the Assertion is true.

Reason:

(a + b)(a – b) = a² – b²

This is a standard algebraic identity and is true.