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Question

Find the smallest number that must be added to get a perfect square.
(i) 2361 (ii) 4931 (iii) 18265 (iv) 390700

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Solution

(i) 2361
2500>2361
50>2361
2401>2361
49>2361
2304<2361
48<2361
2401 is the perfect square nearest to 2361.
24012361=40 is the number to be added.
40 is the least number to be added to 2361 to make it a perfect square.
(ii) 4931
4900<4931
70<4931
5041>4931
71>4931
5041 is the perfect square nearest to 4931.
50414931=110 is the number to be added.
110 is the least number to be added to 4931 to make it a perfect square.
(iii) 18265
18225<18265
135<18265
18496>18265
136>18265
18496 is the perfect square nearest to 18265.
1849618265=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.
(iv) 390700
390625<390700
625<390700
391876>390700
626>390700
391876 is the perfect square nearest to 390700.
391876390700=1176 is the number to be added to 390700.
1176 is the least number to be added to 390700 to make it a perfect square.

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