Question
`(1)/(sqrt(9) - sqrt(8))` - `(1)/(sqrt(8) - sqrt(7))` + `(1)/(sqrt(7) - sqrt(6))` - `(1)/(sqrt(6) - sqrt(5)` + `(1)/(sqrt(5) - sqrt(4))` is equal to :
Answer: Option D
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Given exp. `(1)/(sqrt(9) - sqrt(8))` x `(sqrt(9) + sqrt(8))/(sqrt(9) + sqrt(8))` - `(1)/(sqrt(8) - sqrt(7))` x` ( sqrt(8) + sqrt(7)) /(sqrt(8) + sqrt(7))`+ `(1)/(sqrt(7) -
sqrt(6))` x ` (sqrt(7) + sqrt(6))/(sqrt(7) + sqrt(6))`- `(1)/(sqrt(6) - sqrt(5)` x `(sqrt(6) +sqrt(5))/ (sqrt(6) + sqrt(5))` + `(1)/(sqrt(5) - sqrt(4))` x `(sqrt(5) + sqrt(4))/(sqrt(5) + sqrt(4))`
= `(sqrt(9) + sqrt(8))/(9 - 8)` - `(sqrt(8) - sqrt(7))/(8 - 7)` + `(sqrt(7) + sqrt(6))/(7 - 6)` - `(sqrt(6) + sqrt(5))/(6 - 5)` +
`(sqrt(5) + sqrt(4))/(5 - 4)`
=`(sqrt(9) + sqrt(8)) - (sqrt(8) + sqrt(7)) + (sqrt(7) + sqrt(6)) - (sqrt(6) + sqrt(5)) + (sqrt(5) + sqrt(4))`
=`(sqrt(9) + sqrt(4))` = 3 + 2 = 5.
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