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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. 

 

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