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Question
Compare the following:
`root(3)(48) and sqrt(36)`
Solution
`root(3)(48) = 48^(1/3) "has power" (1)/(3)`
`sqrt(36)` = 6
Now, L.C.M. of 3 and 1 = 3
`root(3)(48) = 48^(1/3)`
`sqrt(36) = 6 = 6^(3/3) = (6^3)^(1/3) = 216^(1/3)`
Since 48 < 216, we have `48^(1/3) < 216^(1/3)`
Hence, `root(3)(48) < sqrt(36)`.
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