`((sqrt(5)-3))/((sqrt(5)-3))times((sqrt(5)-3))/((sqrt(5)+3))`

(5+sqrt(6))/(5-sqrt(6))times(5+sqrt(6))/(5+sqrt 6)

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))

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))

Solve : (4-sqrt(5))/(4+sqrt(5))+ (2)/(5+sqrt(3))+(4+sqrt(5))/(4-sqrt(5))

(1)/(2sqrt(5)-sqrt(3))-(2sqrt(5)+sqrt(3))/(2sqrt(5)+sqrt(3)) =

If x=(sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3)) and y=(sqrt(5)-\ sqrt(3))/(sqrt(5)+\ sqrt(3)) , then x+y+x y= (a) 9 (b) 5 (c) 17 (d) 7

(sqrt(-3))(sqrt(-5)) is equal to

Simplify each of the following : (i) 3/(5-sqrt(3))+2/(5+sqrt(3)) (ii) (4+sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (iii) (sqrt(5)-2)/(sqrt(5)+2)-(sqrt(5)+2)/(sqrt(5)-2)

Find the values of a and b in each of the following : (a)(5+2sqrt3)/(7+4sqrt(3))=a-6sqrt(3)" "(b)(3-sqrt(5))/(3+2sqrt(5))=asqrt(5)-(19)/(11) (c )(sqrt(2)+sqrt(3))/(3sqrt2-2sqrt(3))=2-bsqrt(6)" "(d)(7+sqrt(5))/(7-sqrt(5))-(7-sqrt(5))/(7+sqrt(5))=a+(7)/(11)sqrt(5b)

(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3)) Is equal to :