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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.
1458
Solution
1458 can be factorised as follows:
| 2 | 1458 |
| 3 | 729 |
| 3 | 243 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
1458 = 2 × 3 × 3 × 3 × 3 × 3 × 3
Here, prime factor 2 does not have its pair. If 2 gets a pair, then the number will become a perfect square. Therefore, 1458 has to be multiplied with 2 to obtain a perfect square.
Therefore, 1458 × 2 = 2916 is a perfect square.
1458 × 2 = 2916 = 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3
∴ `sqrt(2916)` = 2 × 3 × 3 × 3 = 54
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