Q. Check which of the following are perfect cubes.

(i) 2700

(ii) 16000

(iii) 64000

(iv) 900

(v) 125000

(vi) 36000

(vii) 21600

(viii) 10,000

(ix) 27000000

(x) 1000.

What pattern do you observe in these perfect cubes?

Answers (1)

The detailed solution for the above-written question is as follows

By prime factorization:

(i)  2700 = 2\times2\times3\times3\times3\times5\times5.      So it is not a perfect cube.

(ii)  16000 = 2\times2\times2\times2\times2\times2\times2\times5\times5\times5.   So it is not a perfect cube.

(iii)  64000 = 2\times2\times2\times2\times2\times2\times2\times2\times2\times5\times5\times5= 80\times80\times80.  So it is a perfect cube.

(iv)  900 = 2\times2\times3\times3\times5\times5.   So it is not a perfect cube.

(v)  125000 = 2\times2\times2\times5\times5\times5\times5\times5\times5.   So it is a perfect cube.

(vi) 36000 = 2\times2\times2\times2\times2\times3\times3\times5\times5\times5.  So it is not a perfect cube.

(vii) 21600 = 2\times2\times2\times2\times2\times3\times3\times3\times5\times5.  So it is not a perfect cube.

(viii) 10000 = 2\times2\times2\times2\times5\times5\times5\times5.  So it is not a perfect cube.

(ix)  27000000 = 2\times2\times2\times2\times2\times2\times3\times3\times3\times5\times5\times5\times5\times5\times5.   So it is a perfect cube.

(x)  1000 = 2\times2\times2\times5\times5\times5.  So it is a perfect cube.

We observe that the numbers above which are perfect cube have the number of zeros in multiple of 3.

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