Evaluate the following: `\ (sqrt(3)+1)^5-(sqrt(3)-1)^5`

Evaluate the following: \ (3+sqrt(2))^5-(3-sqrt(2))^5

Evaluate the following: \ (1+2sqrt(x))^5+(1-2sqrt(x))^5

Evaluate the following: (i) (2 + sqrt(5) )^(5) + (2 - sqrt(5) )^(5) (ii) ( sqrt(3) + 1)^(5) - ( sqrt(3) - 1)^(5) Hence, show in (ii), without using tables, that the value of ( sqrt(3) + 1)^(5) lies between 152 and 153.

Evaluate the following limit: (lim)_(x->1)(sqrt(3+x)-sqrt(5-x))/(x^2-1)

Evaluate the following limit: (lim)_(x->1)(sqrt(3+x)-sqrt(5-x))/(x^2-1)

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))

Evaluate the following limit: (lim)_(x->1)(sqrt(5x-4)-sqrt(x))/(x^3-1)

Rationalise the denominator of each of the following (i) (sqrt(3)+\ 1)/(sqrt(2)) (ii) (sqrt(2)+\ sqrt(5))/(sqrt(3)) (iii) (3sqrt(2))/(sqrt(5))

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)

Using binomial theorem, expand [ ( x+y)^(5) + (x-y)^(5) ] and hence find the value of [ ( sqrt(3) + 1)^(5) - ( sqrt(3) - 1)^(5) ] .