Write the following in the descending order of magnitude.
`root3(2), sqrt(3),root6(5)`

Explanation

We have `root3(2) = 2^((1)/(3)) , sqrt(3) = 3^((1)/(3)),root6(5) = 5^((1)/(6)).`
LCM of 3,2 and 6 = 6.
`therefore 2^((1)/(3)), =2^(((1)/(3) xx (2)/(2)) ) = 2^((2)/(6)) = (2^(2))^((1)/(6)) = 4^((1)/(6)),`
`3^((1)/(2)) = 3^(((1)/(2) xx (3)/(3))) = 3^((3)/(6)) = (3^(3))^((1)/(6)) = (27)^((1)/(6))`.
Clearly , `(27)^((1)/(6)) gt 5^((1)/(6)) gt 4^((1)/(6))`.
So, `3^((1)/(2)) gt 5^((1)/(6)) gt 2^((1)/(3))` or ` sqrt(3) gt root6(5) gt root3(2)`.
Hence, the correct descending order is `sqrt(3), root6(5) and root3(2)`.