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.
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.