`sqrt(((sqrt(12)-sqrt(8)(sqrt(3)+sqrt(2)))/(5+sqrt(24)))` का मान ज्ञात करें।

Options

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

Answer

C

Explanation

`sqrt(([(sqrt(12)-sqrt(8))(sqrt(3)+sqrt(2))]))/(5+sqrt(24))`
`implies sqrt((6-4)/(5+sqrt(24)))`
`impliessqrt(2/(5+sqrt(24))xx(5-sqrt(24))/(5-sqrt(24)))`
`impliessqrt((2(5-sqrt(24)))/(25-24))`
`sqrt(2)(5-2)sqrt(6)))`
`impliessqrt(2((sqrt(3))^(2)+(sqrt(2))^(2)-2sqrt(3)xxsqrt(2)))`
`implies sqrt(2(sqrt(3)-sqrt(2))^(2))`
`implies sqrt(2)(sqrt(3)-sqrt(2))`
`sqrt(6)-2`