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प्रश्न
Find the smallest number by which the following number must be multiplied to obtain a perfect cube.
72
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उत्तर
| 2 | 72 |
| 2 | 36 |
| 2 | 18 |
| 3 | 9 |
| 3 | 3 |
| 1 |
72 = 2 × 2 × 2 × 3 × 3
Here, two 3s are left that are not in a triplet. To make 72 cubes, one more 3 is required.
Then, we obtain
72 × 3 = 2 × 2 × 2 × 3 × 3 × 3 = 216 is a perfect cube.
Hence, the smallest natural number by which 72 should be multiplied to make it a perfect cube is 3.
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