Question

Rationalise the denominator of `3/(4 - sqrt(7))`.

Answer 1

To rationalise the denominator of `3/(4 - sqrt(7))`

Multiply numerator and denominator by the conjugate of the denominator:

`3/(4 - sqrt(7)) xx (4 + sqrt(7))/(4 + sqrt(7)) = (3(4 + sqrt(7)))/((4 - sqrt(7))(4 + sqrt(7))`

Now compute:

Denominator: `(4 - sqrt(7))(4 + sqrt(7))`

= 16 – 7

= 9

Numerator: `3(4 + sqrt(7))`

= `12 + 3sqrt(7)`

So, `(12 + 3sqrt(7))/9`

Now simplify:

= `(3(4 + sqrt(7)))/9`

= `(4 + sqrt(7))/3`