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

The director circle of a hyperbola is x^(2) + y^(2) - 4y =0 . One end of the major axis is (2,0) then a focus is (a) (sqrt(3),2-sqrt(3)) (b) (-sqrt(3),2+sqrt(3)) (c) (sqrt(6),2-sqrt(6)) (d) (-sqrt(6),2+sqrt(6))

Rationalise the denominator and simplify: (i) (4sqrt(3)+5sqrt(2))/(sqrt(48)+\ sqrt(18)) (ii) (2sqrt(3)-\ sqrt(5))/(2\ sqrt(2)+\ 3sqrt(3))

Simplify: (2sqrt(2)+sqrt(3))/(2sqrt(2)-sqrt(3))

Simplify: (i) (3sqrt(2)-2sqrt(2))/(3sqrt(2)+\ 2sqrt(3))+(sqrt(12))/(sqrt(3)-\ sqrt(2)) (ii) (sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3))+(sqrt(5)-\ sqrt(3))/(sqrt(5)+\ sqrt(3))

Show that : (3sqrt(2)-2sqrt(3))/(3sqrt(2)+2sqrt(3))+(2sqrt(3))/(sqrt(3)-sqrt(2))=11

Simplify: 2/(sqrt(5)+\ sqrt(3))+1/(sqrt(3)+\ sqrt(2))-3/(sqrt(5)+\ sqrt(2))

Simplify (sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) e

Rationales the denominator and simplify: (i) (sqrt(3)-\ sqrt(2))/(sqrt(3)\ +\ sqrt(2)) (ii) (5+2\ sqrt(3))/(7+4\ sqrt(3))

Simplify : (7)/(sqrt(17) - 2sqrt3)-( 3)/(sqrt(17) +2sqrt3)

Angles of a triangle are in 4:1:1 ration. The ratio between its greatest side and perimeter is 3/(2+sqrt(3)) (b) (sqrt(3))/(2+sqrt(3)) (sqrt(3))/(2-sqrt(3)) (d) 1/(2+sqrt(3))