Which is the greatest among the following ?
`(sqrt(3))^30, (sqrt(27))^4, (sqrt(81))^8, and (3sqrt(9))^12`

Options

A. `(sqrt(3))^(30)`
B. `(sqrt(27))^(4)`
C. `(3sqrt(9))^(6)`
D. `(sqrt(81))^(8)`

Answer

D

Explanation

`(sqrt(3))^30=(3^(1//2))^30=3^15`
`(sqrt(27))^4=(27^(1//27))^4=27^2=(3^3)^2=3^6`
`(sqrt(18))^8=(81^(1//2))^8=81^4=(3^4)^4=3^16`
`(3sqrt(9))^12=(9^(1//3))^12=(3^(2//3))12=3^(8)`
The greatest among.
`3^15,3^6, and 3^4 is 3^16`, i.e., `(sqrt(81))^8`.
Hence the correct option is (d).