Evaluate using binomial theorem:
`(i) (sqrt(2)+1)^(6) +(sqrt(2)-1)^(6)`
`(ii) (sqrt(5)+sqrt(2))^(4)-(sqrt(5)-sqrt(2))^(4)`

(sqrt(6+2sqrt(5)))(sqrt(6-2sqrt(5)))

(sqrt(6)+sqrt(5)+ 1/(sqrt(6)+sqrt(5)))^2

(sqrt(2)-1)/(sqrt(2))+(3-2sqrt(2))/(4)+(5sqrt(2)-7)/(6sqrt(2))+……oo=

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

Rationalies the denominator and simplify: (i) (1+sqrt(2))/(3-2sqrt(2)) (ii) (2sqrt(6)-\ sqrt(5))/(3sqrt(5)-\ 2sqrt(6))

4^(5log_(4)(sqrt(2)(3-sqrt(6)))-6log_(8)(sqrt(3)-sqrt(2)))

Rationales the denominator and simplify: (1+sqrt(2))/(3-2sqrt(2))( ii) (2sqrt(6)-sqrt(5))/(3sqrt(5)-2sqrt(6))

Simplify each of the following by rationalising the denominator,(1)/(5+sqrt(2)) (ii) (5+sqrt(6))/(5-sqrt(6)) (iii) (7+3sqrt(5))/(7-3sqrt(5)) (iv) (2sqrt(3)-sqrt(5))/(2sqrt(2)+3sqrt(3))

(ii) log_(sqrt(5)+1)(6+2sqrt(5))