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Question
Find the cube root of the following numbers by the prime factorisation method.
27000
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Solution
| 2 | 27000 |
| 2 | 13500 |
| 2 | 6750 |
| 3 | 3375 |
| 3 | 1125 |
| 3 | 375 |
| 5 | 125 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factorisation of 27000 = 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 5
= 23 × 33 × 53 = (2 × 3 × 5)3
∴ `root3 (27000)`
= 2 × 3 × 5 = 30
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