Sol.   `sqrt(86.49) + sqrt(5 + x^2) = 12.3`

         Then ,` 9.3 + sqrt(5 + x^2) = 12.3`   

         `hArr      sqrt(5 + x^2) = 12.3 - 9.3`

         `hArr       sqrt(5 + x^2) = 3`

          `hArr       5 + x^2 = 9`

           `hArr       x^2 = 9 - 5 = 4`

            `hArr        x^2 = 4`

             `hArr       x = sqrt(4)`

           `hArr          x = 2`

Sol.      Let  `sqrt(32.4/x)  = 2`

             Then , `32.4/x = 4`

`hArr      4x = 32.4`

  `hArr       x = 8.1 `        

Sol.     `sqrt(0.0009)`

             = `sqrt(9/10000)`

             = `sqrt(9)/sqrt(10000)`

             = ` 3/100`     = 0.03   

Sol.       `sqrt(1 9/16)`

          = `sqrt(25/16)`

          = `5/4 =  1 1/4`

Sol.    6 * 15 * 3 = `(sqrt((6+ 2) ( 15 + 3)))/(3 + 1)`

                           = `sqrt(8 xx 18)/4`

                          = `sqrt(144)/4` =  `12/4` = 3.

Sol.    Given expression  = `sqrt(248 +sqrt(51 +sqrt(169)))`

                                         = `sqrt(248 + sqrt(51 + 13))`

                                         = `sqrt(248 + sqrt(64))`

                                          = ` sqrt(248 + 8)`

                                           = `sqrt(256)`

                                            = 16. 

3600 = `2^3 xx 5^2 xx 3^2 xx `2.

To make it a perfect cube , it must be divided by `5^2 xx 3^2 xx 2 ` i.e. , 450.

675 = 5 x 5 x 3 x 3 x 3

To make it  a perfect cube, it must be multiplied by 5.

Clearly , 9261 is a perfect cube satisfying the given property.

`sqrt(.000064)` = `sqrt(64/10^6)` =  `8/10^3` = `8/1000` = .008

`:.`  `3sqrt(sqrt (.000064))` = `3sqrt(.008)` = `3sqrt(8/1000)` = `2/10` = 0.2