(iii) `(sqrt(4)-sqrt(3))^(2)`

Rationales the denominator and simplify: (4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18))( ii) (2sqrt(3)-sqrt(5))/(2sqrt(2)+3sqrt(3))

Simplify the following expressions: (4+sqrt(7))(3+sqrt(2))( (ii) (3+sqrt(3))(5-sqrt(2))(sqrt(5)-2)(sqrt(3)-sqrt(5))

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))

Let the length of latus rectum of an ellipse with its major axis along x-axis and center at the origin,be 8. If the distance between the foci of this ellipse is equal to the length of the minor axis,then which of the following points lies on it: (a) (4sqrt(2),2sqrt(2)) (b) (4sqrt(3),2sqrt(2)) (c) (4sqrt(3),2sqrt(3))( d) (4sqrt(2),2sqrt(3))

(i) 3sqrt(5) by 2sqrt(5) ,(ii) 6sqrt(15) by 4sqrt(3) , (iii) 2sqrt(6) by 3sqrt(3) (iv) 3sqrt(8) by 3sqrt(2) ,(v) sqrt(10) by sqrt(40) , (vi) 3sqrt(28) by 2sqrt(7)

Simplify the following expressions: (4+sqrt(7))(3+sqrt(2))( ii) (3+sqrt(3))(5-sqrt(2))(sqrt(5)-2)(sqrt(3)-sqrt(5))(sqrt(5)+sqrt(2))(sqrt(3)+sqrt(2))

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

Examine,whether the following numbers are rational or irrational: sqrt(7) (ii) sqrt(4) (iii) 2+sqrt(3)

Find (a+b)^(4)-(a-b)^(4). Hence evaluate (sqrt(3)+sqrt(2))^(4)-(sqrt(3)-sqrt(2))^(4)