Sum of decimal places in the numerator and  denominator under the radical sign being the same, we remove the

decimal.

`:.`  Given exp =    `sqrt((.081 xx .484)/(.0064 xx 6.25))` = `sqrt((81 xx 484)/(64 xx 625))`

                        =  `(9 xx 22)/(8 xx 25)` =  0.99

`(3sqrt(12))/(2sqrt(28))` `-:` `(2sqrt(21))/(sqrt(98))` =`(3sqrt(12))/(2sqrt(28))` x `(sqrt(98))/(2sqrt(21))`

 =`(3sqrt(4 xx 3))/(2sqrt(4 xx 7))` x` (sqrt(49 xx 2))/(2sqrt(21))` =  `(6sqrt(3))/(4sqrt(7))` x `(7sqrt(2))/(2sqrt(21))`

= `(21sqrt(6))/(4sqrt(7 xx 21))` =   `(21sqrt(6))/(28sqrt(3))`     = `3/4`` sqrt(2)`=  `3/4` x 1.414 =  3 x 0.3525 = 1.0605

Given exp. = `sqrt(8) + 2sqrt(32) - 3sqrt(128) + 4sqrt(50)`

                  = `sqrt(4 xx 2) + 2sqrt(16 xx 2) - 3sqrt(64 xx 2) + 4sqrt(25 xx 2)`

                 = `2sqrt(2) + 8sqrt(2) - 24sqrt(2) + 20sqrt(2)`     = `6sqrt(2)`  =  6 x 1.414 = 8.484. 

`sqrt(50) xx sqrt(98)` =  `sqrt(50 xx 98)` = `sqrt(4900)` = 70.

`3sqrt(5) + sqrt(125)`  = 17.88,    `rArr` ` 3sqrt(5) + sqrt(25 xx 5)`  =  17.88

   `rArr`  `3sqrt(5) + 5sqrt(5)` = 17.88    `rArr` ` 8sqrt(5)` = 17.88    `rArr` ` sqrt(5) `=  2.235.

`:.`  `sqrt(80) + 6sqrt(5)` =  `sqrt(16 xx 5) + 6sqrt(5)` = `4sqrt(5) + 6sqrt(5)` =  `10sqrt(5)`

= (10 x 2.235) =  22.35

`(sqrt(80) - sqrt(112))/ (sqrt(45) - sqrt(63))`  = `(sqrt(16 xx 5) - sqrt(16 xx 7))/(sqrt(9 xx 5) - sqrt(9 xx 7))`

= `(4sqrt(5) - 4sqrt(7))/(3sqrt(5) - 3sqrt(7))` = `(4(sqrt(5) - sqrt(7)))/(3(sqrt(5) - sqrt(7)))` =  `4/3` =  `1 1/3`

`(sqrt(24) + sqrt(216))/(sqrt(96))`  = `(sqrt(4 xx 6) + sqrt(36 xx 6))/(sqrt(16 xx 6))`

= `(2sqrt(6) + 6sqrt(6))/(4sqrt(6))` =`(8sqrt(6))/(4sqrt(6))` =  2

`(sqrt(12) + sqrt(18)) - (sqrt(3) + sqrt(2))` = `(sqrt(4xx3) +sqrt(9xx2)) - (sqrt(3) + sqrt(2))`

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

= `sqrt(3) + 2sqrt(2)`.

`(2sqrt(27) - sqrt(75) + sqrt(12))` = `2sqrt(9 xx 3) - sqrt(25 xx 3) + sqrt(4 xx 3)`

                 = `6sqrt(3) - 5sqrt(3) + 2sqrt(3)`  =  `3sqrt(3)`

`sqrt(1 + 55/729)` = 1 + `x/27`  `rArr` `sqrt(784/729)` =  `(27 + x)/(27)` `rArr` `28/27` =` (27 + x)/(27)`

                            `rArr`  27 + `x` = 28  `rArr`  `x` = 1.