(7)/(3sqrt(3)-2sqrt(2))

(2sqrt(7))/(sqrt(5)-sqrt(3))

Add (i) (2sqrt(3)-5sqrt(2)) and (sqrt(3) + 2sqrt(2)) (ii) (2sqrt(2) + 5sqrt(3) - 7 sqrt(5) and (3sqrt(3)-sqrt(2) + sqrt(5)) (iii) ((2)/(3) sqrt(7) -(1)/(2)sqrt(2)+6sqrt(11)) and ((1)/(3)sqrt(7) + (3)/(2)-sqrt(11))

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))

(sqrt(3)-sqrt(5))(sqrt(3)+sqrt(5))/(sqrt(7)-2sqrt(5))

7sqrt(3)+2sqrt(27)

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 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 by raationalising the denominator. (i) (7sqrt(3) - 5sqrt(2))/(sqrt(48) + sqrt(18)) (ii) (2sqrt(6) -sqrt(5))/(3sqrt(5)-2sqrt(6))

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

(sqrt(7)+2sqrt(3))(sqrt(7)-2sqrt(3))