Question

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) 525 (ii) 1750

Answer 1

(i) The square root of 525 can be calculated by long division method as follows.

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 √529 = 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 √1764 = 42