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Question
Find the cube root of the following number by the prime factorisation method.
512
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Solution
| 2 | 512 |
| 2 | 256 |
| 2 | 128 |
| 2 | 64 |
| 2 | 32 |
| 2 | 16 |
| 2 | 8 |
| 2 | 4 |
| 2 | 2 |
| 1 |
Prime factorisation of 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 23 × 23 × 23 = (2 × 2 × 2)3
∴ `root3 512` = 2 × 2 × 2
= 8
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