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प्रश्न
For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
1008
उत्तर
1008 can be factorised as follows:
| 2 | 1008 |
| 2 | 504 |
| 2 | 252 |
| 2 | 126 |
| 3 | 63 |
| 3 | 21 |
| 7 | 7 |
| 1 |
1008 = 2 × 2 × 2 × 2 × 3 × 3 × 7
Here, prime factor 7 does not have its pair. If 7 gets a pair, then the number will become a perfect square. Therefore, 1008 can be multiplied with 7 to obtain a perfect square.
1008 × 7 = 7056 = 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7
Therefore, 1008 × 7 = 7056 is a perfect square.
∴ `sqrt(7056)` = 2 × 2 × 3 × 7 = 84
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