(iii) `(2+sqrt(6))/(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))

Simplify: (i) (2 sqrt(2) + 3 sqrt(3)) (2 sqrt(2) - 3 sqrt(3)) (ii) (2 sqrt(8) - 3 sqrt(2))^(2) (iii) (sqrt(7) + sqrt(6))^(2) (iv) (6 - sqrt(2))(2 + sqrt(3))

Express each one of the following with rational denominator: (sqrt(3)+1)/(2sqrt(2)-sqrt(3))( ii) (6-4sqrt(2))/(6+4sqrt(2))

(2sqrt(6))/(sqrt(2)+sqrt(3)+sqrt(5)) equals

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

(2sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3))-(8sqrt(3))/(sqrt(6)+sqrt(2))

The value of 5sqrt(3) + 7sqrt(2) - sqrt(6) - 23/(sqrt(2) + sqrt(3) + sqrt(6)) is:

If the direction cosines of two lines are (1)/(sqrt(6)),(-1)/(sqrt(6)),(2)/(sqrt(6))and(2)/(sqrt(6)),(1)/(sqrt(6)),(-1)/(sqrt(6)) respectively, then the acute angle between them is

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