Q:

# Is zero a perfect square?

A:

There is some dispute as to whether zero is a perfect square. It meets most definitions of a perfect square, namely that it is an integer squared. However, it does not meet the historical definition of a perfect square, which involves arranging objects in a square shape.

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A perfect square is the product of an integer multiplied by itself. For example, three times three equals nine. Nine is therefore a perfect square. Zero times zero equals zero, suggesting that zero is a perfect square. However, the historical definition requires that objects can be arranged in a square. Nine objects can be arranged in a 3x3 square. Zero objects cannot be arranged in a square.

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