Question

(6 + root27)/(4 - root3) can be written in the form (r + sroot3)/13

Answer 1

r = 33 , s = 18

Explanation:

Rationalise the denominator by multiplying both numerator and denominator by the conjugate of the denominator.

The conjugate of 4 -
`√(3)` is 4 +
`√(3)` , then

`((6+√(27))(4+√(3)) )/((4-√(3))(4+√(3)) )` ← expand numerator/denominator using FOIL

=
`(24+6√(3)+4√(27)+√(81) )/(16+4√(3)-4√(3)-3 )`

=
`(24+6√(3)+4(3√(3)+9 )/(16-3)`

=
`(33+6√(3)+12√(3) )/(13)`

=
`(33+18√(3) )/(13)`

with r = 33 and s = 18