Question

Rationalise the denominator

Answer 1

30 + 12
`√(5)`

Explanation:

To rationalise the denominator, multiply the numerator and denominator by the conjugate of the denominator.

The conjugate of 2
`√(5)` - 4 is 2
`√(5)` + 4 , then

`(12√(5)(2√(5)+4) )/((2√(5)-4)(2√(5)+4) )` ← expand denominator using FOIL

=
`(120+48√(5) )/(20-16)`

=
`(120+48√(5) )/(4)` ( divide each term on numerator by 4 )

= 30 + 12
`√(5)`

Answer 2

30+12(square root of 5)

Explanation: