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Question
Compare: `root(6)(15) and root(4)(12)`
Solution
`root(6)(15) = (15)^(1/6) and root(4)(12) = (12)^(1/4)`
Make powers `1/6 and 1/4` same
L.C.M. of 6, 4 is 12
`1/6 xx 2/2 = 2/12 and 1/4 xx 3/3 = 3/12`
⇒ `root(6)(15) = 15^(1/6) = 15^(2/12) = (15^2)^(1/12) = 225^(1/12)`
and `root(4)(12) = 12^(1/4) = 12^(3/12) = (12^3)^(1/12) = (1728)^(1/12)`
⇒ 1728 > 225
⇒ `(1728)^(1/12) > 225^(1/12)`
⇒ `root(4)(12) > root(6)(15)`
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