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Rationalise the denomimator of (6)/(sqrt...

Rationalise the denomimator of `(6)/(sqrt(5)+ sqrt(2))`

A

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

B

`3(sqrt(5) -sqrt(2))`

C

`2(sqrt(5) -sqrt(2))`

D

`2(sqrt(5) +sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
We have
` (6)/((sqrt(5)+sqrt(2)) ) = (6)/((sqrt(5) + sqrt(2))) xx ((sqrt(5)-sqrt(2)))/((sqrt(5) - sqrt(2))) = (6(sqrt(5)-sqrt(2)))/((sqrt(5))^(2) -(sqrt(2))^(2))`
`(6(sqrt(5)-sqrt(2)))/(5-2) = (6(sqrt(5)-sqrt(2)))/(5-2) = (6sqrt(5)-sqrt(2))/(3) = 2(sqrt(5) -sqrt(2))`
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