L.C.M. of  3, 4, 5, 6, 8 is 120, Now  120 = 2 x 2 x 2 x 3 x 5.

To make it a perfect square, is must be multiplied by  2 x 3 x 5

So required number = `2^2 xx 2^2 xx 3^2 xx 5^2` =  3600

Clearly , `a ** b ` = `sqrt(a^2 + b^2)`

`:.`  `5**12` = `sqrt(5^2 + 12^2)` = `sqrt(25 + 144)` = `sqrt(169)` = 13.

`sqrt(5)/2 - 10/sqrt(5) + sqrt(125)` = `(sqrt(5)^2 - 20 + 2sqrt(5) xx 5sqrt(5))/(2sqrt(5))`

                                                      =  `(5 - 20 + 50)/(2sqrt(5))` = `(35)/(2sqrt(5))`

                                                      = `(35)/(2sqrt(5))`  x  `sqrt(5)/sqrt(5)` =   `(35sqrt(5))/(10)`

                                                      =  `7/2`  x 2.236 =   7 x 1.118 =  7.826 

`(3sqrt(2))/(2sqrt(3))` = `(3sqrt(2))/(2sqrt(3))` x `sqrt(3)/sqrt(3)` =  `(3sqrt(6))/(2xx3)` =  `sqrt(6)/2` = `2.449/2` = 1.2245.

`sqrt(8/3)` = `sqrt((8 xx 3)/(3 xx 3))`  = `sqrt(24)/3` =  `4.899/3`  = 1.633

`1/sqrt(5)` = `1/sqrt(5) xx sqrt(5)/sqrt(5)` = `sqrt(5)/5 ` = `2.236/5` =  0.447

`(1 + sqrt(0.01))/(1 - sqrt(0.1))`  = `(1 + 0.1)/(1 - 0.316)` = `1.1/0.684`

= `1100/684`   = 1.6

`sqrt(0.16/0.4)` = `sqrt(0.16/0.40)` = `sqrt(16/40)`= `sqrt(4/10)` = `sqrt(0.4)` =  0.63.

`sqrt(0.09)` =   `sqrt(9/100)` =  `3/10` =  0.3, which is rational.

`:.`  0.09 has rational square root.

`sqrt(0.overline(4))` = `sqrt(4/9)` =  `2/3` =   0.666............ = `0. overline(6)`