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Which of the following rational numbers is Not a perfect cube?

A. 827

B. 12564

C. − 64

D. 136



1 Answer

3 votes

Answer: Choice D

We have 8/27 which can be written as (2/3)^3, so 8/27 is a perfect cube.

Similarly, 125/64 = (5/4)^3, showing that it too is a perfect cube. So far we have eliminated choices A and B.

Choice C is also eliminated because -64 = (-4)^3

Lastly, choice D is not a perfect cube assuming it is 136 because 136^(1/3) = 5.142563 is not rational (ie not a fraction of whole numbers). The same can be said about 1/36 and 13/6 as well.

User Adam Lee Perelman
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