`1/(sqrt(3)+sqrt(4))+1/(sqrt(4)+sqrt(5))+1/(sqrt(5)+sqrt(6))`
`+1/(sqrt(6)+sqrt(7))+1/(sqrt(7)+sqrt(8))+1/(sqrt(8)+sqrt(9))` का मान ज्ञात करें।

Options

A. `sqrt(3)`
B. `3sqrt(3)`
C. `3-sqrt(3)`
D. `5-sqrt(3)`

Answer

C

Explanation

`1/(sqrt(3)+sqrt(4))`
`implies1/(sqrt(4)+sqrt(3))xx(sqrt(4)-sqrt(3))/(sqrt(4)-sqrt(3))`
`implies(sqrt(4)-sqrt(3))/1`
`impliessqrt(4)-sqrt(3)`
similarly
`implies1/(sqrt(4)+sqrt(4))=sqrt(5)-sqrt(4)`
`implies1/(sqrt(5)+sqrt(6))impliessqrt(6)-sqrt(5)`
`implies1/(sqrt(6)+sqrt(7))impliessqrt(7)-sqrt(6)`
`implies1/(sqrt(7)+sqrt(8))=sqrt(8)-sqrt(7)`
`implies1/(sqrt(8)-sqrt(9))impliessqrt(9)-sqrt(8)`
Now put values
`impliessqrt(4)-sqrt(3)+sqrt(5)-sqrt(4)+sqrt(6)-sqrt(5)+sqrt(7)-`
`sqrt(6)+sqrt(8)-sqrt(7)-sqrt(9)-sqrt(8)`
`implies sqrt(9)-sqrt(3)`
`implies3-sqrt(3)`