# Find the least number which must be added to each of the following numbers so as to get a perfect square.

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Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.

(i) 252 (ii) 1825 (ii) 6412

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(i) 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 256 = 16

(ii) 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 The required perfect square is 1849 and 1849 = 43

(iii) 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 The required perfect square is 6561 and 6561 = 81