Question

Rationalise the denominator of `(3sqrt(3) - 2)/(2sqrt(7) + 1)`.

Answer 1

Let’s rationalise the expression:

`(3sqrt(3) - 2)/(2sqrt(7) + 1)`

Step 1: Multiply numerator and denominator by the conjugate of the denominator `(2sqrt(7) - 1)`:

`(3sqrt(3) - 2)/(2sqrt(7) + 1) xx (2sqrt(7) - 1)/(2sqrt(7) - 1)`

Step 2: Simplify Denominator

`(2sqrt(7) + 1)(2sqrt(7) - 1)`

= `(2sqrt(7))^2 - 1^2`

= 4 × 7 – 1

= 28 – 1

= 27

Step 3: Expand the Numerator

`(3sqrt(3) - 2)(2sqrt(7) - 1)`

1. `3sqrt(3) xx 2sqrt(7)`

= `6sqrt(21)`

2. `3sqrt(3) xx (-1)`

= `-3sqrt(3)`

3. `-2 xx 2sqrt(7)`

= `-4sqrt(7)`

4. `-2 xx (-1)`

= 2

So the numerator becomes:

`(6sqrt(21) - 3sqrt(3) - 4sqrt(7) + 2)/27`