Question

Rationalise the denominator:

`(sqrt(5) + 2)/(sqrt(5) - 2)`

Answer 1

We are asked to rationalise:

`(sqrt(5) + 2)/(sqrt(5) - 2)`

Step 1: Multiply numerator and denominator by the conjugate of the denominator:

`(sqrt(5) + 2)/(sqrt(5) - 2) xx (sqrt(5) + 2)/(sqrt(5) + 2) = (sqrt(5) + 2)^2/((sqrt(5))^2 - 2^2)`

Step 2: Simplify numerator:

`(sqrt(5) + 2)^2`

= `(sqrt(5))^2 + 2 xx sqrt(5) xx 2 + 2^2`

= `5 + 4sqrt(5) + 4`

= `9 + 4sqrt(5)` 

Step 3: Simplify denominator:

`(sqrt(5))^2 - (2)^2`

= 5 – 4

= 1

`(9 + 4sqrt(5))/1`

= `9 + 4sqrt(5)`