Sarthaks Test
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Which of the following numbers are notperfect cubes?

(i) 100   (ii) 46656

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(i) The prime factorisation of 100 is as follows.

2100
250
525
55
1

100 = 2 × 2 × 5 × 5

Here, each prime factor is not appearing as many times as a perfect multiple of 3. Two 2s and two 5s are remaining after grouping the triplets. Therefore, 100 is not a perfect cube.

(ii) The prime factorisation of 46656 is as follows.

246656
223328
211664
25832
22916
21458
3729
3243
381
327
39
33
1

46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

Here, as each prime factor is appearing as many times as a perfect multiple of 3, therefore, 46656 is a perfect cube.

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