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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.
2028
Solution
2028 can be factorised as follows:
| 2 | 2028 |
| 2 | 1014 |
| 3 | 507 |
| 13 | 169 |
| 13 | 13 |
| 1 |
2028 = 2 × 2 × 3 × 13 × 13
Here, prime factor 3 does not have its pair. If 3 gets a pair, then the number will become a perfect square. Therefore, 2028 has to be multiplied with 3 to obtain a perfect square.
Therefore, 2028 × 3 = 6084 is a perfect square.
2028 × 3 = 6084 = 2 × 2 × 3 × 3 × 13 × 13
∴ `sqrt(6084)` = 2 × 3 × 13 = 78
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