Question
Which is larger `sqrt(2)` or`root3(3)` ?
Answer: Option A
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Sol. Given surds are of order 2 and 3. Their L.C.M. is 6
Changing each to a surd of order 6, we get :
`sqrt(2) = 2^(1/2) = 2^(1/2 xx 3/3) = (2^3)^(1/6) = (8)^(1/6) = root6(8)`
`3sqrt(3) = 3^(1/3) = 3^(1/3 xx 2/2) = 3^(2/6) = (3^2)^(1/6)= root6(9)`
Clearly `, root6(9) > root6(8) ` and hence `root3(3) > sqrt(2)`
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