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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.
180
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Solution
180 can be factorised as follows:
| 2 | 180 |
| 2 | 90 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
180 = 2 × 2 × 3 × 3 × 5
Here, prime factor 5 does not have its pair. If 5 gets a pair, then the number will become a perfect square. Therefore, 180 has to be multiplied with 5 to obtain a perfect square.
180 × 5 = 900 = 2 × 2 × 3 × 3 × 5 × 5
Therefore, 180 × 5 = 900 is a perfect square.
∴ `sqrt(900)` = 2 × 3 × 5 = 30.
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