`(sqrt(7) + sqrt(5))/(sqrt(7) - sqrt(5))`= `(sqrt(7) + sqrt(5))/(sqrt(7) - sqrt(5))` x `(sqrt(7) + sqrt(5))/(sqrt(7) + sqrt(5))`

`((sqrt(7) + sqrt(5))^2) /((7 - 5))` =  `(7 + 5 + 2sqrt(35))/(2)` =  `(12 + 2sqrt(35))/(2)` = ` 6 + sqrt(35)`

`(3sqrt(2))/(sqrt(6) - sqrt(3))`  x `((sqrt(6) + sqrt(3)))/((sqrt(6) + sqrt(3)))`  - `(4sqrt(3))/((sqrt(6) - sqrt(2)))` x `((sqrt(6) + sqrt(2)))/((sqrt(6) + sqrt(2)))` - `(6)/(2(sqrt(2) - sqrt(3)))`

=` (3sqrt(2)(sqrt(6) + sqrt(3))) /((6 - 3))`  - ` (4sqrt(3)(sqrt(6) + sqrt(2)))/ ((6 - 2))` +` (3)/(sqrt(3)- sqrt(2))`  x `((sqrt(3) + sqrt(2)))/((sqrt(3) + sqrt(2)))`

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

=`sqrt(12) + sqrt(6) - sqrt(18) - sqrt(6) + 3sqrt(3) + 3sqrt(2)`

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

`(7)/((3 + sqrt(2)))` = `(7)/((3 + sqrt(2)))` x `((3  - sqrt(2)))/((3 - sqrt(2)))`

`(7(3 - sqrt(2)))/((9 - 2))` = ` (3 - sqrt(2))` =   (3 - 1.4142) =  1.5858

Given exp. =  `(2 + sqrt(2))` + `(1)/((2 + sqrt(2)))` x   ` ((2 - sqrt(2)))/((2 - sqrt(2)))` - `(1)/((2 - sqrt(2)))` x `((2 + sqrt(2)))/((2 + sqrt(2)))`

=`(2 + sqrt(2))` + `((2 - sqrt(2)))/((4 - 2))` - `((2 + sqrt(2)))/((4 - 2))`

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

Given exp. `(1)/(sqrt(9) - sqrt(8))`  x `(sqrt(9) + sqrt(8))/(sqrt(9) + sqrt(8))` - `(1)/(sqrt(8) - sqrt(7))` x` ( sqrt(8) + sqrt(7)) /(sqrt(8) + sqrt(7))`+ `(1)/(sqrt(7) -
sqrt(6))` x ` (sqrt(7) + sqrt(6))/(sqrt(7) + sqrt(6))`- `(1)/(sqrt(6) - sqrt(5)`  x `(sqrt(6) +sqrt(5))/ (sqrt(6) + sqrt(5))`  + `(1)/(sqrt(5) - sqrt(4))` x `(sqrt(5) + sqrt(4))/(sqrt(5) + sqrt(4))`

= `(sqrt(9) + sqrt(8))/(9 - 8)` - `(sqrt(8) - sqrt(7))/(8 - 7)` + `(sqrt(7) + sqrt(6))/(7 - 6)` - `(sqrt(6) + sqrt(5))/(6 - 5)` +

`(sqrt(5) + sqrt(4))/(5 - 4)`

=`(sqrt(9) + sqrt(8)) - (sqrt(8) + sqrt(7)) + (sqrt(7) + sqrt(6)) - (sqrt(6) + sqrt(5)) + (sqrt(5) + sqrt(4))`

=`(sqrt(9) + sqrt(4))`  =  3 + 2 = 5.

`(1)/(sqrt(5) - sqrt(3))` = `(1)/(sqrt(5) - sqrt(3))` x `(sqrt(5) - sqrt(3))/(sqrt(5) - sqrt(3))`

= `(sqrt(5) - sqrt(3))/(5 - 3)` =  `(2.2361 + 1.7321)/(2)` =  `3.9682/2` =  1.9841.

1470=  7 x 7 x 5 x 6 . To make it a perfect square . it must be divided by  5 x 6, i.e. , 30

5808 = 2 x 2 x 2 x 2 x 3 x 11 x 11 =  `2^2 xx 2^2 xx 3 xx 11^2`

To make it a  perfect square it must be multiplied by 3.

294 =  7 x 7 x 2 x 3.

To make it a perfect square , it must be multiplied by 2 x 3  i.e.  6

`:.`  Required number = 6.

L.C.M. of 21, 36, 66 =  2772, Now 2772 =  2 x 2 x 3 x 3 x 7 x 11

To make it a perfect square it must be multiplied by 7 x 11 .

So required number = `2^2xx 3^2 xx 7^2 xx 11^2` =  213444