`(2/(sqrt(6)+2)+1/(sqrt(7)+sqrt(6))+1/(sqrt(8)-sqrt(7))+2-2sqrt(2))` के बराबर है।

Options

A. 0
B. `2sqrt(2)`
C. `sqrt(2)`
D. `2sqrt(7)`

Answer

D

Explanation

`2/(sqrt(6)+2)+1/(sqrt(7)+sqrt(6))+1/(sqrt(8)-sqrt(7))+2-2sqrt(2)`
`implies2/(sqrt(6)+2)xx(sqrt(6)-2)/(sqrt(6)-2)+1/(sqrt(7)+sqrt(6))xx(sqrt(7)-sqrt(6))/(sqrt(7)-sqrt(6))+`
`1/(sqrt(8)-sqrt(7))xx(sqrt(8)+sqrt(7))/(sqrt(8)-sqrt(7))+2-2sqrt(2)`
`implies(2xx(sqrt(6)-2))/(6-4)+((sqrt(7)-sqrt(6)))/(7-6)+(sqrt(8)+sqrt(7))/(8-7)`
`+2-2sqrt(2)`
`impliessqrt(6)-2+sqrt(7)-sqrt(6)+sqrt(8)+sqrt(7)+2-2sqrt(2)`
`impliessqrt(6)-2+sqrt(7)+2sqrt(2)+sqrt(7)+2-2sqrt(2)`
`=2sqrt(7)`