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The number obtained on rationalising the...

The number obtained on rationalising the denominator of `(1)/(sqrt(7) - 2)` is

A

`(sqrt(7) + 2)/(3)`

B

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

C

`(sqrt(7) + 2)/(5)`

D

`(sqrt(7) + 2)/(45)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(1)/(sqrt(7) - 2) = (1)/(sqrt(7) - 2) . (sqrt(7) + 2)/(sqrt(7) + 2)` , [multiplying numerator and denominator by `sqrt(7) + 2`]
`= (sqrt(7) + 2)/((sqrt(7))^(2) - (sqrt(2))^(2)) = (sqrt(7) +2)/(7-4) = (sqrt(7) +2)/(3)` [using identity `(a-b) (a+b) = a^(2) - b^(2)`]
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