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Question
Find the cube root of the following number by the prime factorisation method.
46656
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Solution
| 2 | 46656 |
| 2 | 23328 |
| 2 | 11664 |
| 2 | 5832 |
| 2 | 2916 |
| 2 | 1458 |
| 3 | 729 |
| 3 | 243 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factorisation of 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3
= 23 × 23 × 33 × 33
= (2 × 2 × 3 × 3)3
∴ `root3 (46656)`
= 2 × 2 × 3 × 3
= 36
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