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Rationalise the denominator of (1)/((8+5...

Rationalise the denominator of `(1)/((8+5sqrt(2))`.

A

` ((8-5sqrt(2)))/(12)`

B

` ((8-5sqrt(2)))/(14)`

C

`((8+5sqrt(2)))/(14)`

D

` ((8-5sqrt(2)))/(34)`

Text Solution

Verified by Experts

The correct Answer is:
B
We have
`(1)/((8+sqrt(2)))= (1)/((8+5sqrt(2))) xx ((8-5sqrt(2)))/((8-5sqrt(2))) =((8-5sqrt(2)))/((8)^(2) - (5sqrt(2))^(2))`
`= ((8-2sqrt(2)))/(64-50) = ((8-5sqrt(2)))/(14)`
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