Question

Write the following in ascending order:

`2root(3)(3), 4root(3)(3) and 3root(3)(3)`

Answer 1

Since `2root(3)(3) = root(3)(2^3 xx 3) = root(3)(8 xx 3) = root(3)(24)`
`4root(3)(3) = root(3)(4^3 xx 3) = root(3)(64 xx 3) = root(3)(192)`
`3root(3)(3) = root(3)(3^3 xx 3) = root(3)(27 xx 3) = root(3)(81)`
Since, 24 < 81 < 192, we have `root(3)(24) < root(3)(81) < root(3)(192)`.
Hence, `2root(3)(3) < 3root(3)(3) < 4root(3)(3)`.