`(27 6-sqrt(6 3/4))^2+(2(sqrt(2)+sqrt(6)))/(3sqrt(2+sqrt(3)))`

The value of (6sqrt(27)-sqrt(6(3)/(4)))^(2)+(2(sqrt(2)+sqrt(6)))/(3sqrt(2+sqrt(3))) is

If a=(4sqrt(6))/(sqrt(2)+sqrt(3))

(3+sqrt(6))/(sqrt(3)+sqrt(2))

(3-sqrt(6))/(3+2sqrt(6))=a sqrt(6)-b

(3sqrt(2))/(sqrt(3)+sqrt(6))-(4sqrt(3))/(sqrt(6)+sqrt(2))+(sqrt(6))/(sqrt(3)+sqrt(2))

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))

Rationales the denominator and simplify: (sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) (ii) (5+2sqrt(3))/(7+4sqrt(3)) (iii) (1+sqrt(2))/(3-2sqrt(2)) (2sqrt(6)-sqrt(5))/(3sqrt(5)-2sqrt(6)) (v) (4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18)) (vi) (2sqrt(3)-sqrt(5))/(2sqrt(3)+3sqrt(3))