Recognize perfect squares

A perfect square is a nonnegative integer that can be expressed as the product of an integer by itself, such as $25=5\times5$ , and can be represented by a square array with equal side lengths. The learner recognizes common perfect squares, typically from $0$ through $144$ , identifies their whole-number square roots, and distinguishes them from numbers whose square roots are not whole numbers; generalized or very large cases and irrational square roots are not included.

Detailed Explanation: Recognize perfect squares

A perfect square is a number made by multiplying a whole number by itself:

n \times n=n^2.

To recognize one:

Think of a whole number that might be its square root.
Multiply that number by itself.
If the product matches the given number, it is a perfect square.
The number you multiplied is the whole-number square root.

Worked example: Is $(81)$ a perfect square?

Try $9$ , because $9$ is a common square root:

9 \times 9=81.

So,

81=9^2.

Therefore, $(81)$ is a perfect square, and its whole-number square root is

\sqrt{81}=9.

You can also picture $(81)$ objects arranged in a square array with $9$ rows and $9$ columns. Equal side lengths show that $(81)$ is a square number.

Learn by doing: Recognize perfect squares

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Squares - Is Number a Perfect Square

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