Question
Check whether 21600 is a perfect cube or not.
✓
Answer
Given number is 21600.
Now, prime factorisation of 21600
$\therefore 21600=\underline{2 \times 2 \times 2} \times \underline{3 \times 3 \times 3}\times 2 \times 2 \times 5 \times 5$
Prime factors 2 and 5 do not have triples.
So, 21600 is not a perfect cube.
Now, prime factorisation of 21600
$\therefore 21600=\underline{2 \times 2 \times 2} \times \underline{3 \times 3 \times 3}\times 2 \times 2 \times 5 \times 5$
| 2 | 21600 |
| 2 | 10800 |
| 2 | 5400 |
| 3 | 2700 |
| 3 | 900 |
| 3 | 300 |
| 2 | 100 |
| 2 | 50 |
| 5 | 25 |
| 5 | 5 |
| 1 |
So, 21600 is not a perfect cube.
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