`(sqrt(2))/(sqrt(3)+sqrt(6))-(4sqrt(3))/(sqrt(6)+sqrt(2))+(sqrt(6))/(sqrt(3)+sqrt(2))` का सरलीकृत मान क्‍या है?

Options

A. `sqrt(2)`
B. `1/(sqrt(2))`
C. `sqrt(3)-sqrt(2)`
D. `0`

Answer

D

Explanation

`(3sqrt(2))/(sqrt(3)+sqrt(6))-(4sqrt(3))/(sqrt(6)+sqrt(2))+(sqrt(6))/(sqrt(3)+sqrt(2))`
`=(3sqrt(2)(sqrt(6)-sqrt(3)))/3-(4sqrt(3)(sqrt(6)-sqrt(2)))/4`
`+(sqrt(6)(sqrt(3)-sqrt(2)))/1`
`=2sqrt(3)-sqrt(6)-3sqrt(2)+sqrt(6)+3sqrt(2)-2sqrt(3)`
`=0`