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Rationalise (6-4sqrt(3))/(6+4sqrt(3))...

Rationalise `(6-4sqrt(3))/(6+4sqrt(3))`

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Verified by Experts

We have
`(6-4sqrt(3))/(6+sqrt(3)) = ((6-4sqrt(3)))/((6+ 4sqrt(3)))xx ((6-sqrt(2)))/((6-4sqrt(3))) = ((6-4sqrt(3))^(2))/((6)^(2) - (4sqrt(3))^(2))`
`= (6^(2) + (4sqrt(3))^(2) - 2xx6xx4sqrt(3)0)/(36-48) = (36+48-48sqrt3)/(-12)`
`= (84-48sqrt(3))/(-12) = (48sqrt(3) - 84)/(12) = (4sqrt(3) - 7)`
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