Q. 54.1( 105 Votes )

Find the least nu

Answer :

(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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