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Question

For each of the following, find the least number that must be added so that the resulting number is a perfect square.

(i) 511       (ii) 7172         (iii) 55078


Solution

(i) 511

Taking square root of 511, We find that 27 has been left

We see that 511 is greater than 222

On adding the required number to 511, we get (23)2 i.e., 529

So, the required number = 529-511=18

(ii) 7172

Taking square root of 7172, We find that 116 has been left

We see that 7172 is greater than (84)2

On adding the required number to 7172, we get (85)2 i.e., 7225

Required number = 7225- 7172 = 53

(iii) 55078

 

Taking square root of 55078, We find that 322 has been left

We see that 55078 is greater than (234)2

On adding the required number to 55078, we get (235)2 i e., 55225

Required number = 55225 - 55078 = 147

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