Perfect Square

Perfect Square

A number that is the square of a whole number.


16 is a perfect square because 4² = 16 and 4 is a whole number.

20 is not a perfect square because \(\sqrt {20}\) is not a whole number.

Educational Note

The expression “perfect square” should not be applied to any algebraic expression.

So, the trinomial x² – 4x + 4 which is equal to (x – 2)² can only be called a perfect square if x – 2 is a whole number. Instead, we should say that the trinomial x² – 4x + 4 is the square of the binomial (x – 2).

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