Indices, SMB-031

Rationalise the denominator of the surd fraction `(8-2sqrt(6))/(3sqrt(2)+2sqrt(3))`. (3 marks)

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`6sqrt(2)-14/3sqrt(3)`

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`(8-2sqrt(6))/(3sqrt(2)+2sqrt(3))`

`=(8-2sqrt(6))/(3sqrt(2)+2sqrt(3))xx(3sqrt(2)-2sqrt(3))/(3sqrt(2)-2sqrt(3))`

`=((8-2sqrt(6))(3sqrt(2)-2sqrt(3)))/((3sqrt(2))^2-(2sqrt(3))^2)`

`=(24sqrt(2)-16sqrt(3)-6sqrt(12)+4sqrt(18))/(18-12)`

`=(24sqrt(2)-16sqrt(3)-12sqrt(3)+12sqrt(2))/6`

`=(36sqrt(2)-28sqrt(3))/6`

`=6sqrt(2)-14/3sqrt(3)`