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Question

Which of the following numbers are cubes of rational numbers:
(i)2764(ii)125128(iii)0.001331(iv)0.04

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Solution

(i)2764=3×3×34×4×4=(34)32764 is a perfect cube
(ii)125128=5×5×52×2×2×2×2×2×2=(5)3(2)3×(2)3×2
We see that 128 is not a perfefct cube
125128 is not a perfect cube.
(iii)0.001331=13311000000=11×11×1110×10×10×10×10×10=(1110×10)3=(11100)3
It is a perfect cube.

(iv)0.04=4100=2×210×10=210×210or0.2×0.2
or 0.2 is not in triplet.


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