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प्रश्न
Using prime factorisation, find the cube roots of 512
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उत्तर
First we have to find out the factors by using prime factorisation method.
| 2 | 512 |
| 2 | 256 |
| 2 | 128 |
| 2 | 64 |
| 2 | 32 |
| 2 | 16 |
| 2 | 8 |
| 2 | 4 |
| 2 | 2 |
| 1 |
So, prime factors of 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Now, grouping the prime factors = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2)
Then, cube root of `512 = root(3)(512)`
= `root(3)((2 xx 2 xx 2) xx (2 xx 2 xx 2) xx (2 xx 2 xx 2))`
= `root(3)(2^3 xx 2^3 xx 2^3)`
= 2 × 2 × 2
= 8
∴ The cube root of 512 is 8.
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