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Find the smallest positive integer that must be added to 2010 to obtain a perfect square (a square of an integer)

User Eric Milas
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Final answer:

The smallest positive integer that must be added to 2010 to obtain a perfect square is 45.

Step-by-step explanation:

To find the smallest positive integer that must be added to 2010 to obtain a perfect square, we need to consider the properties of perfect squares. A perfect square is a number that can be expressed as the square of an integer. We can use trial and error to find the smallest positive integer that, when added to 2010, results in a perfect square.

Starting with 2010, we can add 1, 2, 3, and so on until we find a perfect square. By doing this, we can determine that adding 45 to 2010 yields a perfect square: 2010 + 45 = 2055, and the square root of 2055 is approximately 45.36.

Therefore, the smallest positive integer that must be added to 2010 to obtain a perfect square is 45.

User Lander Van Breda
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