Perfect Square: Definition, Formula & Examples

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  • 0:05 Definition of a Perfect Square
  • 0:55 Creating Perfect Squares
  • 2:26 Lesson Summary
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Lesson Transcript
Instructor: Joseph Vigil
In this lesson, you'll learn what perfect squares are and view a few examples of them. You'll also discover the formula for creating perfect squares. Then, you can test your new knowledge with a brief quiz.

Definition of a Perfect Square

When Danielle gets bored in class, she doodles by making squares out of dots. By the end of her first class, she has this on her paper:

1, 4, 9, and 16 dots arranged in squares.

Each group of dots happens to be a square because they all have the same number of dots going vertically as they do going horizontally.

If we counted the number of dots in each of Danielle's squares, we get the following totals:

1, 4, 9, and 16 dots arranged in squares.

1, 4, 9, and 16 are perfect squares, or square numbers, because we can arrange those numbers of items into squares.

We could represent each square as a multiplication sentence using the number of dots in the rows and columns:

1 4 9 and 16 represented as squares and as multiplication sentences

Danielle thought she was simply doodling, but it seems she's on to something!

Creating Perfect Squares

Of course, Danielle could go on doodling bigger and bigger squares forever, so there are infinite perfect squares. The list definitely doesn't stop with 16. She wouldn't have to draw all those squares, though, to determine the next perfect square.

We can see that any number multiplied by itself creates a perfect square. Again, this is because a square's length and width are equal, so the dots in the square's rows and columns will always be equal.

We left off at 16, or 4 * 4. So to determine the next perfect square, we would continue the pattern:

5 * 5 = 25

The next perfect square after 16 is 25.

We can check that with another model:

a square of 25 dots

We could even determine the hundredth perfect square if we want to!

100 * 100 = 10,000

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