Question

Rationalise the denominator of the following:

`1/(sqrt(6) - sqrt(5))`

Answer 1

Given:

`1/(sqrt(6) - sqrt(5))`

Step-wise calculation:

1. Multiply by the Conjugate:

Multiply both the numerator and denominator by the conjugate of the denominator, which is `sqrt(6) + sqrt(5)`:

`1/(sqrt(6) - sqrt(5)) xx (sqrt(6) + sqrt(5))/(sqrt(6) + sqrt(5))`

= `(sqrt(6) + sqrt(5))/((sqrt(6) - sqrt(5))(sqrt(6) + sqrt(5))`

2. Simplify the Denominator:

Apply the difference of squares formula (a – b)(a + b) = a² – b²:

`(sqrt(6))^2 - (sqrt(5))^2`

= 6 – 5

= 1

3. Final Expression:

`(sqrt(6) + sqrt(5))/1 = sqrt(6) + sqrt(5)`

The rationalized form of `1/(sqrt(6) - sqrt(5))` is `sqrt(6) + sqrt(5)`.