Question

Rationalise the denominator of the following:

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

Answer 1

Given: `(sqrt(2) + 1)/(sqrt(2) - 1)`

Step-wise calculation:

Multiply the numerator and denominator by the conjugate of the denominator `sqrt(2) + 1`: 

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

= `(sqrt(2) + 1)^2/((sqrt(2))^2 - (1)^2`

Calculate numerator and denominator:

`(sqrt(2) + 1)^2`

= `(sqrt(2))^2 + 2 xx sqrt(2) xx 1 + 1^2`

= `2 + 2sqrt(2) + 1`

= `3 + 2sqrt(2)`

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

= 2 – 1

= 1

So, `(3 + 2sqrt(2))/1 = 3 + 2sqrt(2)`.