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प्रश्न
Find the smallest number by which of the following number must be multiplied to obtain a perfect cube.
100
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उत्तर
| 2 | 100 |
| 2 | 50 |
| 5 | 25 |
| 5 | 5 |
| 1 |
100 = 2 × 2 × 5 × 5
Here, two 2s and two 5s are left, which are not in a triplet. To make 100 a cube, we require one more 2 and one more 5.
Then, we obtain
100 × 2 × 5 = 2 × 2 × 2 × 5 × 5 × 5 = 1000 is a perfect cube
Hence, the smallest natural number by which 100 should be multiplied to make it a perfect cube is 2 × 5 = 10.
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