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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