# Which of the following numbers are notperfect cubes? (i) 216 (ii) 128 (ii) 1000

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Which of the following numbers are notperfect cubes?

(i) 216 (ii) 128 (ii) 1000

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(i) The prime factorisation of 216 is as follows.

 2 216 2 108 2 54 3 27 3 9 3 3 1

216 = 2 × 2 × 2 × 3 × 3 × 3 = 23 × 33

Here, as each prime factor is appearing as many times as a perfect multiple of 3, therefore, 216 is a perfect cube.

(ii)The prime factorisation of 128 is as follows.

 2 128 2 64 2 16 2 8 2 4 2 2 1

128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

Here, each prime factor is not appearing as many times as a perfect multiple of 3. One 2 is remaining after grouping the triplets of 2. Therefore, 128 is not a perfect cube.

(iii) The prime factorisation of 1000 is as follows

 2 1000 2 500 2 250 5 125 5 25 5 5 1

1000 = 2 × 2 × 2 × 5 × 5 × 5

Here, as each prime factor is appearing as many times as a perfect multiple of 3, therefore, 1000 is a perfect cube.

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