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Question
Find the least number which must be added to the following number so as to get a perfect square. Also find the square root of the perfect square so obtained.
1750
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Solution
The square root of 1750 can be calculated by long division method as follows:
| 41 | |
| 4 | `bar17 bar50` -16 |
| 81 | 150 -81 |
| 69 |
The remainder is 69.
Clearly, 412 = 1681 < 1750
422 = 1764 > 1750.
Hence, the number to be added is 1764 − 1750 = 14, and the square root of 1764 is 42.
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