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Question
For the following number, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained.
2800
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Solution
2800 can be factorised as follows.
| 2 | 2800 |
| 2 | 1400 |
| 2 | 700 |
| 2 | 350 |
| 5 | 175 |
| 5 | 35 |
| 7 | 7 |
| 1 |
2800 = 2 × 2 × 2 × 2 × 5 × 5 × 7
Here, prime factor 7 does not have its pair.
If we divide this number by 7, the number will become a perfect square.
Therefore, 2800 has to be divided by 7 to obtain a perfect square.
2800 ÷ 7 = 400 is a perfect square.
400 = 2 × 2 × 2 × 2 × 5 × 5
∴ `sqrt400` = 2 × 2 × 5 = 20
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