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Question
Find the smallest number by which the following number must be divided to obtain a perfect cube.
81
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Solution
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
81 = 3 × 3 × 3 × 3
Here, one 3 is left, which is not in a triplet.
If we divide 81 by 3, then it will become a perfect cube.
Thus, 81 ÷ 3
= 27
= 3 × 3 × 3 is a perfect cube.
Hence, the smallest number by which 81 should be divided to make it a perfect cube is 3.
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