# Find the least nu

(i) The square root of 525 can be calculated by long division method as: The remainder is 41

It represents that the square of 22 is less than 525

Next number is 23 and 232 = 529

Hence, number to be added to 525 = 232 - 525

= 529 - 525

= 4

The required perfect square is 529 and = 23

(ii) The square root of 1750 can be calculated by long division method as follows: The remainder is 69

It represents that the square of 41 is less than 1750

The next number is 42 and 422 = 1764

Hence, number to be added to 1750 = 422– 1750

= 1764 - 1750

= 14

The required perfect square is 1764 and = 42

(iii) The square root of 252 can be calculated by long division method as follows: The remainder is 27. It represents that the square of 15 is less than 252

The next number is 16 and 162 = 256

Hence, number to be added to 252 = 162 - 252

= 256 - 252

= 4

The required perfect square is 256 and = 16

(iv) The square root of 1825 can be calculated by long division method as follows: The remainder is 61. It represents that the square of 42 is less than 1825

The next number is 43 and 432 = 1849

Hence, number to be added to 1825 = 432 - 1825

= 1849- 1825

= 24

Hence, number to be added to 1825 = 24

The required perfect square is 1849 and = 43

(v) The square root of 6412 can be calculated by long division method as follows: The remainder is 12. It represents that the square of 80 is less than 6412

The next number is 81 and 812 = 6561

Hence, number to be added to 6412= 812 - 6412

= 6561- 6412

= 149

Hence, number to be added to 6412= 149

The required perfect square is 6561 and = 81

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