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Question
Write the following in ascending order:
`2root(3)(3), 4root(3)(3) and 3root(3)(3)`
Solution
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)`.
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