Question
The largest number from among `sqrt(2), root3(3) and root4(4)` is :
Answer: Option B
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L.C.M. of 2, 3, 4 is 12
`sqrt(2) = 2^(1/2) = 2^((1/2 xx 6/6)) = 2^(6/12) = (2^6)^(1/12) = (64)^(1/12) = root12(64)`
`root3(3) = 3^(1/3) = 3^((1/3 xx 4/4)) = 3^(4/12) = (3^4)^(1/12) = (81)^(1/12) = root12(81)`
`root4(4) = 4^(1/4) = 4^((1/4 xx 3/3)) = 4^(3/12) = (4^3)^(1/12 )= (64)^(1/12) = root12(64)`
Clearly, `root12(81), i.e. , root3(3) ` is the largest.
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