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Question
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.
768
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Solution
768 can be factorised as follows:
| 2 | 768 |
| 2 | 384 |
| 2 | 192 |
| 2 | 96 |
| 2 | 48 |
| 2 | 24 |
| 2 | 12 |
| 3 | 6 |
| 13 |
768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
Here, prime factor 3 does not have its pair. If 3 gets a pair, then the number will become a perfect square. Therefore, 768 has to be multiplied with 3 to obtain a perfect square.
Therefore, 768 × 3 = 2304 is a perfect square.
768 × 3 = 2304 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
∴ `sqrt(2304)` = 2 × 2 × 2 × 2 × 3 = 48
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