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Question
Compare the following:
`root(4)(12) and root(3)(15)`
Solution
`root(4)(12) = 12^(1/4) "has power" (1)/(4)`
`root(3)(15) = 15^(1/3) "has power" (1)/(3)`
Now, L.C.M. of 4 and 3 = 12
`root(4)(12) = 12^(1/4) = 12^(3/12) = (12^3)^(1/12) = (1728)^(1/12)`
`root(3)(15) = 15^(1/3) = 15^(4/12) = (15^4)^(1/12) = (50625)^(1/12)`
Since 1728 < 50625, we have `(1728)^(1/12) < (50625)^(1/12)`.
Hence, `root(4)(12) < root(3)(15)`.
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