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High School Trigonometry: Homework Help Resource30 chapters | 203 lessons

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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.

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:

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 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:

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

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:

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

100 * 100 = 10,000

So, the one hundredth perfect square is 10,000.

We could say that the formula for creating a perfect square is

*x* ** x*

Where *x* is any integer. And if we want to determine a specific perfect square, we can simply plug in that value for *x*. We wanted to know the hundredth perfect square, so we multiplied 100 * 100.

A **perfect square** is any number that can be represented by a square consisting of the same number of rows and columns. The formula for creating a perfect square is:

*x* * *x*

Where *x* is any integer. To determine a certain perfect square, we would simply plug that value in for *x*. That's why we plugged in 100 for *x* when we wanted to determine the hundredth perfect square.

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Lesson
6 in chapter 22 of the course:

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High School Trigonometry: Homework Help Resource30 chapters | 203 lessons

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