Expand by using suitable identity:
`(sqrt{3}+1/sqrt{3})^2`

Using suitable identity, evaluate: (97)^(3)

Using suitable identity, evaluate: (104)^(3)

Remove the irrationality in the denominator a. sqrt((sqrt(2)-1)/(sqrt(2)+1)) b. 1/(1+sqrt(2)+sqrt(3))

(sqrt(3)-1/(sqrt(3)))^2 is equal to

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

Simplify: (sqrt3/2)^2 -(sqrt3)^2+(sqrt 2)^2 +1/2

Solve: (sqrt 3+ sqrt2)(sqrt2-sqrt3)

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.

Rationalize the denominatior of : (1)/(sqrt(3)-sqrt(2))

Rationalize the denominator: (2 + sqrt 3)/(2 - sqrt 3) + (2 - sqrt 3)/(2 + sqrt 3) + (sqrt 3 - 1)/(sqrt 3 + 1)