Page 2 - Lesson Note

Example 1: Find the least number that must be subtracted from 5607 so as to get
a perfect square. Also find the square root of the perfect square.

Solution: Let us try to find √5607 by long division method. We get the
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remainder 131. It shows that 74 is less than √5607 by 131.
This means if we subtract the remainder from the number,
we get a perfect square.
Therefore, the required perfect square is 5607 – 131 = 5476. And, √5476= 74

Example 2:Find the least number that must be added to 1300 so as to get a
perfect square. Also find the square root of the perfect square.

Solution: We find √1300 by long division method. The remainder is 4.

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This shows that 36 < 1300.
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Next perfect square number is 37 = 1369.
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Hence, the number to be added is 37 – 1300 = 1369 – 1300 = 69.