The descending order of `root(3)(4),sqrt2,root(6)(3)` and `root(4)(5)` is

Options

A. `root(3)(4) gt root(4)(5) gt sqrt(2) gt root(6)(3)`
B. `root(3)(5) gt root(3)(4), gt root(6)(3) gt sqrt(2)`
C. `sqrt(2) gt root(6)(3) gt root(3)(4) gt root(4)(5)`
D. `root(6)(3) sqrt(2) gt root(3)(4) gt sqrt(2)`

Answer

A

Explanation

`(4)^(1/3) . (2)^(2/3) = 8^(8/12) = (256)^(1/12)`
`(2)^(1/2) = 2^(6/12) = (64)^(1/2)`
`(3)^(1/6) = 3^(2/12) = 9^(1/12)`
`(5)^(1/4) = (5)^(3/12) = (125)^(1/12)`
अवरोही क्रम में सजाने परः
`(4)^(1/3) gt (5)^(1/4) gt 2^(1/2) gt (3)^(1/6)`