Find the least number which must be added to the following numbers to make them a perfect square:
(i) 5607
(ii)4931
(iii) 4515600
(iv) 37460
(v) 506900
(i) 5607
The remainder is 131
Hence, (74)2 < 5607
The next perfect square number is:
(75)2 = 5625 > 5607
Hence, the number to be added = 5625 – 5607
= 18
The remainder is 31
Hence, (70)2 < 4931
The next perfect square number is:
(71)2 = 5041 > 4931
Hence, the number to be added = 5041 – 4931
= 110
The remainder is 4224
Hence, (2124)2 < 4515600
The next perfect square number is:
(2125)2 = 4515625 > 4515600
Hence, the number to be added = 4515625 – 4515600
= 25
The remainder is 211
Hence, (193)2 < 37460
The next perfect square number is:
(194)2 = 37636 > 37460
Hence, the number to be added = 37636 – 37460
= 176
The remainder is 1379
Hence, (711)2 < 506900
The next perfect square number is:
(712)2 = 506944 > 506900
Hence, the number to be added = 506944 – 506900
= 44