i) 4931
4900 < 4931
⇒ 70 < sq root of 4931
5041 > 4931
⇒ 71 > sq root of 4931
⇒ 5041 is the perfect square nearest to 4931.
⇒ 5041 – 4931 = 110 is the number to be added.
∴ 110 is the least number to be added to 4931 to make it a perfect square.
ii) 2361
2500 > 2361
⇒ 50 > sq root of 2361
2401 >2361
⇒ 49 > sq root of 2361
2304 < 2361
⇒ 48 < sq root of 2361
∴ 2401 is the perfect square nearest to 2361.
∴ 2401 – 2361 = 40 is the number to be added.
∴ 40 is the least number to be added to 2361 to make it a perfect square.
iii) 18265
18225 < 18265
⇒ 135 < sq root of 18265
18496 > 18265
⇒ 136 > sq root of 18265
⇒ 18496 is the perfect square nearest to 18265.
⇒ 18496 – 18265 = 231 is the number to be added to 18265.
∴ 231 is the least number to be added to 18265 to make it a perfect square.