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Question
Find the smallest number by which 200 should be multiplied to make it a perfect cube
Solution
| 2 | 200 |
| 2 | 100 |
| 2 | 50 |
| 5 | 25 |
| 5 | 5 |
| 1 |
We find 200 = `bar(2 xx 2 xx 2) xx 5 xx 5`
Grouping the prime factors of 200 as triplets, we are left with 5 × 5
We need one more 5 to make it a perfect cube.
So to make 200 a perfect cube multiply both sides by 5.
200 × 5 = `(bar(2 xx 2 xx 2) xx 5 xx 5) xx 5`
1000 = 2 × 2 × 2 × 5 × 5 × 5 × 5 × 5
Now 1000 is a perfect cube.
∴ The required number is 5.
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