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Question
Write the following in descending order:
`sqrt(6), root(3)(8) and root(4)(3)`
Solution
Since `sqrt(6) = 6^(1/2) "has power" (1)/(2)`,
`root(3)(8) = 2`
`root(4)(3) = 3^(1/4) "has power" (1)/(4)`
Now, L.C.M. of 2, 1 and 4 = 4
∴ `sqrt(6) = 6^(1/2) = 6^(2/4) = (6^2)^(1/4) = (36)^(1/4)`
`root(3)(8) = 2 = 2^(4/4) = (2^4)^(1/4) = (16)^(1/4)`
`root(4)(3) = 3^(1/4) = (3^1)^(1/4) = (3)^(1/12)`
Since, 36 > 16 > 3, we have `(36)^(1/4) > (16)^(1/4) > (3)^(1/12)`.
Hence, `sqrt(6) > root(3)(8) > root(4)(3)`.
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