Question
Find the sum of the expression
`1/(sqrt(1) + sqrt(2))` + `1/(sqrt(2) + sqrt(3))` + `1/(sqrt(3) + sqrt(4))` +..... +`1/(sqrt(80) + sqrt(81))`
Answer: Option B
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`1/(sqrt(1) + sqrt(2))` + `1/(sqrt(2) + sqrt(3))` + `1/(sqrt(3) + sqrt(4))` +..... +`1/(sqrt(80) + sqrt(81))`
= `(sqrt(2) - sqrt(1))/((sqrt(2))^2 - (sqrt(1))^2)` + `(sqrt(3) - sqrt(2))/((sqrt(3))^2 - (sqrt(2))^2)` + `(sqrt(4) - sqrt(3))/((sqrt(4))^2 - (sqrt(3))^2)` +..... + `(sqrt(81) - sqrt(80))/((sqrt(81))^2 - (sqrt(80))^2)`
= `sqrt(81)` - `sqrt(1)` = 8
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