Simplified value of the following exppression is
`1/(sqrt(11-2sqrt(30)))-2/(sqrt(7-2sqrt(10)))-4/(sqrt(8-4sqrt(3)))`

Options

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

Answer

A

Explanation

`1/(sqrt(11-2sqrt(30)))-3/(sqrt(7)-2sqrt(10))`
`4/(sqrt(8-4sqrt(3)))`
`=1/((sqrt(sqrt(6)-sqrt(5))^(2)))-3/(sqrt((sqrt(5)-sqrt(2))^(2)))`
`-4/(sqrt(2(4-2sqrt(3)))`
`=1/(sqrt(6)-sqrt(5))-3/(sqrt(5)-sqrt(2))`
`-4/((sqrt(2))xxsqrt((sqrt(3)-1)^(2)))`
`implies 1/(sqrt(6)-sqrt(5))-3/(sqrt(5)-sqrt(2))-(2sqrt(2))/(sqrt(3)-1)`
Rationalising all the factors
`=sqrt(6)+sqrt(5)-(3(sqrt(5)+sqrt(2)))/(5-2)`
`-(2sqrt(2)(sqrt(3)+1))/(3-1)`
`=sqrt(6)+sqrt(5)-sqrt(5)-sqrt(2)-sqrt(6)-sqrt(2)`
`=-sqrt(2)`