`:.`  `sqrt(a^2 + b^2 + c^2)` =  `sqrt((a + b + c)^2 - 2(ab + bc + ca))`

= `sqrt((27sqrt(29))^2 - 2(2c xx 3/2 c + 4/2 c xx c  + c xx 2c))`

=`sqrt((729xx 29) - 2(3c^2 + 3/2 c^2 + 2c^2))`

= `sqrt((729 xx 29) - 2 xx 13/2 c^2)`

=`sqrt((729 xx 29) - 13 xx (6sqrt(29))^2)`

= `sqrt(29(729  - 468))`

=`sqrt(29 xx 261)` = `sqrt(29 xx 29 xx 9)` =   29 x 3 =  87.

`((0.75)^3)/(1 - 0.75)` + [0.75 +` (0.75)^2` + 1]

=`sqrt(((0.75)^3 + (1 - 0.75) [(1)^2 + (0.75)^2 + 1 xx 0.75])/(1 - 0.75))`

=`sqrt(((0.75)^3 + [(1)^3 - (0.75)^3])/( 1 - 0.75))` =  `sqrt(1/0.25)` =  `sqrt(100/25)` =  `sqrt(4)` = 2

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

`sqrt((1 + 2a)^2) + 3a` =  (1 - 2a) + 3a =  (1 + a) = (1 + 0.1039) =  1.1039.

`(sqrt(2) + 1/sqrt(2))^2` = `(sqrt(2))^2 + (1/sqrt(2))^2 + 2 xx sqrt(2) xx 1/sqrt(2)` =  2 + `1/2` + 2 = 4+ `1/2` = `4 1/2`

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

= 3 +` 1/3`- 2 = 1 + `1/3` = `4/3`

`sqrt((7 + 3sqrt(5)) (7 - 3sqrt(5)))` = `sqrt((7)^2 - (3sqrt(5))^2)` =  ` sqrt(49 - 45)` = `sqrt(4)` = 2.

Given exp. = `sqrt(((0.03)^2 + (0.21)^2  + (0.065)^2)/((0.003)^2 + (0.021)^2+ (0.0065)^2))`

=`sqrt(((0.03)^2 + (0.21)^2  + (0.065)^2)/((0.03/10)^2 + (0.21/10)^2+ (0.065/10)^2))`

=`sqrt((100[(0.03)^2 + (0.21)^2 + (0.065)^2])/((0.03)^2 + (0.21)^2 + (0.065)^2))` = `sqrt(100) `= 10

Given exp. = `sqrt((9.5 xx 0.85)/(.0017 xx .19))` = `sqrt((9.5 xx .08500)/(.19 xx .0017))`

= `sqrt((95 xx 8500)/(19 xx 17))` =  `sqrt(5 xx 500)` =  `sqrt(2500)` =  50.

Given exp. = `sqrt((81 xx 324 xx 4624)/(15625 xx 289 xx 729 xx 64))`

                 = `(9 xx 18 xx 68)/(125 xx 17 xx 27 xx 8)`=  `3/125`=  0.024.

 Given exp.`sqrt((0.204 xx 42)/(0.07 xx 3.4))` =  `sqrt((204 xx 42)/(7 xx34))` = ` sqrt(36)` =  6.