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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.
252
Solution
252 can be factorised as follows:
| 2 | 252 |
| 2 | 126 |
| 3 | 63 |
| 3 | 21 |
| 7 | 7 |
| 1 |
252 = 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, 252 has to be multiplied with 7 to obtain a perfect square.
252 × 7 = 2 × 2 × 3 × 3 × 7 × 7
Therefore, 252 × 7 = 1764 is a perfect square.
∴ `sqrt(1764)` = 2 x 3 x 7 = 42
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