`3sqrt(4 12/125)` =  `3sqrt(512/125)` =  `((8xx8xx8)/(5xx5xx5))^(1/3)` =   `8/5` =  `1 3/5`

`(.000216)^(1/3)` =  `((216)/(10^6))^(1/3)` =  `((6 xx 6 xx6)/(10^2 xx 10^2 xx10^2))^(1/3)`

= `(6)/(10^2)` =  `6/100` =  .06

Money collected = (59.29 x 100) paise=  5929 paise.

`:.`   Number of members = `sqrt(5929)` = 77.

a = `(sqrt(5) + 1)/(sqrt(5) - 1)`  x `(sqrt(5) + 1)/(sqrt(5) +1)` = `((sqrt(5) + 1)^2)/((5 - 1))`

= `(5 + 1 + 2sqrt(5))/(4)` =  `((3 + sqrt(5))/(2))`

b= `(sqrt(5) - 1)/(sqrt(5) +1)`  x  `(sqrt(5) - 1)/(sqrt(5) -1)` = `((sqrt(5)  - 1)^2)/((5 - 1))` = `(5 + 1 - 2sqrt(5))/(4)`

= `((3 - sqrt(5))/(2))`

`:.`  `a^2 + b^2` = `((3 + sqrt(5))^2)/(4)` + `((3 - sqrt(5))^2)/(4)` = `((3 + sqrt(5))^2 +(3 - sqrt(5))^2)/(4)`

`(2(9 + 5))/(4)`   = 7.

Also, ab = `((3 + sqrt(5) (3 - sqrt(5))/(2)`  = ` (9 - 5)/4` = 1

`:.` ` (a^2 + ab + b^2)/(a^2 - ab + b^2)` =   `((a^2 b^2) + ab)/((a^2 + b^2) - ab)`  =  `(7 + 1)/(7 - 1)` = `8/6` = `4/3`

`x` = `((sqrt(3) + 1))/((sqrt(3) - 1))  xx ((sqrt(3) + 1))/((sqrt(3) +1)) ` = `((sqrt(3) + 1)^2)/((3 - 1 ))`

 = `(3 + 1 + 2sqrt(3))/(2)` = 2 + `sqrt(3)`

y = `((sqrt(3) - 1))/((sqrt(3)+1))  xx ((sqrt(3) -1))/((sqrt(3)-1)) ` = `((sqrt(3) - 1)^2)/((3 - 1))`

= `(3 + 1 -  2sqrt(3))/(2)` =   `2 - sqrt(3)`

`:.`  `x^2 + y^2` = ` (2 + sqrt(3))^2 + (2 - sqrt(3))^2` =   2(4 + 3) = 14.

`x + 1/x` = `(7 - 4sqrt(3)) + (1)/((7 - 4sqrt(3)))  xx ((7 + 4sqrt(3)))/((7 + 4sqrt(3)))`

=` (7 - 4sqrt(3)) + ((7 + 4sqrt(3)))/((49 - 48))`

=`(7 - 4sqrt(3)) + (7 + 4sqrt(3))`   = 14

Given exp.  `(2 + sqrt(3))/(2 - sqrt(3))  xx (2 + sqrt(3))/(2 +sqrt(3))  + (2  - sqrt(3))/(2 + sqrt(3))  xx  (2 -sqrt(3))/(2 - sqrt(3))   + (sqrt(3) - 1)/(sqrt(3) + 1) xx   (sqrt(3) - 1)/(sqrt(3) + 1) `         

=`(( 2 + sqrt(3))^2)/(4 - 3)  + ((2 - sqrt(3))^2)/((4 - 3))  + ((sqrt(3) - 1)^2)/((3 - 1))`

=`[(2 + sqrt(3))^2 + (2 - sqrt(3))^2]  + (4 -2sqrt(3))/(2)`

=` 2(4 + 3) + 2 - sqrt(3)`        = `16 - sqrt(3)`                                         

Given exp. =  `(3 + sqrt(6))/(5sqrt(3) - 4sqrt(3) - 4sqrt(2)  + 5sqrt(2))`  = `((3 + sqrt(6)))/((sqrt(3) + sqrt(2)))`

= `((3 + sqrt(6)))/((sqrt(3) + sqrt(2)))`  x  `((sqrt(3) - sqrt(2)))/((sqrt(3) - sqrt(2)))`

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

`(sqrt(2) - 1)/(sqrt(2) + 1)` = `(sqrt(2) - 1)/(sqrt(2) + 1)` x `(sqrt(2) - 1)/(sqrt(2) -1)`

= `(sqrt(2) - 1)^2`

`:.` ` sqrt( (sqrt(2) - 1)/(sqrt(2) + 1))` = `(sqrt(2) - 1)` = (1.414 - 1 )=  0.414

`a + bsqrt(3)` =  `(5 + 2sqrt(3))/(7 + 4sqrt(3))` x `(7 -  4sqrt(3))/(7 - 4sqrt(3))`

`(35 - 20sqrt(3) + 14sqrt(3) - 24)/((7)^2 - (4sqrt(3))^2)` =  `(11 - 6sqrt(3))/(49 - 48)` =  `11 - 6sqrt(3)`

`:.`  a = 11, b = - 6