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State, with reason, which of the followi...

State, with reason, which of the following are surds and which are not (i) `sqrt(180)` (ii) `(27)^(1/4)` (iii) `(64)^(1/3)`

Text Solution

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If a number after simplification do not become a whole number, then it is a surd.
(i) `sqrt180 = 13.4164`, which is not a whole number.
So, it is a surd.
(ii) `27^(1/4) = (3^3)^(1/4) = 3^(3/4)`, which is not a whole number.
So, it is a surd.
(iii)`64^(1/3) = (4^3)^(1/3) = 4`, which is a whole number.
So, it is not a surd.
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