`sqrt(11+2sqrt(30))-1/(sqrt(11+2sqrt(30))` का मान ज्ञात करें।

Options

A. `2sqrt(5)`
B. `2sqrt(6)`
C. `1+sqrt(6)`
D. `1+sqrt(5)`

Answer

A

Explanation

`sqrt(11+2sqrt(30))-1/(sqrt(11+2sqrt(30)))`
`impliessqrt((sqrt(6))^(2)+(sqrt(5))^(2)+2sqrt(6).sqrt(5))`
`-1/(sqrt((sqrt(6))^(2)+(sqrt(5))^(2)+2sqrt(6).sqrt(5)))`
`impliessqrt((sqrt(6)+sqrt(5))^(2))-1/(sqrt((sqrt(6)+sqrt(5))^(2)))`
`impliessqrt(6)+sqrt(5)-1/(sqrt(6)+sqrt(5))`
Relationalising above question
`impliessqrt(6)+sqrt(5)-1/(sqrt(6)+sqrt(5))xx(sqrt(6)-sqrt(5))/(sqrt(6)-sqrt(5))`
`impliessqrt(6)+sqrt(5)-(sqrt(6)-sqrt(5))`
`impliessqrt(6)+sqrt(5)-sqrt(6)+sqrt(5)`
`implies2sqrt(5)`