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What is the least number that should be added to each of the following to make these perfect squares?

1) 3169

2) 2765

3) 36,320

4) 81,180

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80,44,161,45

84,44,161,45

80,44,163,45

None of these

answer is A.

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Detailed Solution

Concept-
(i) 3169
The square number that is closest to 3169 is 3249, and the difference between the two will be represented as follows:

As a result, we may conclude that 80 should be the lowest number that, when added to 3169, will result in a perfect square.
Hence,

(ii) 2765
The nearest square number to 2765 is 2809, making the difference between the two of them as follows:

As a result, 44 should be the lowest number that can be added to 2765 to create a perfect square.
Hence, $Question Image$ (iii) 36,320
The square number that is closest to 36,320 is 36,481, hence the difference between the two will be reported as-

As a result, 161 should be the lowest number that can be added to 36,320 to create a perfect square.
Hence,

(iv) 81,180
The square number that is closest to 81,180 is 81,225, and the difference between the two of them is as follows:

Since 81,180 plus 45 will result in a perfect square, we may conclude that 45 should be the minimum number.
Hence,

Hence, option 1 is correct.

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