Perfect Squares

Contributor: Erika Wargo. Lesson ID: 12825

Do you feel like a square when it comes to multiplication? Don't squares have to do with geometry? You'll learn how to find the perfect square while "rooting" through interactives and a fun project!


Expressions and Equations, Pre-Algebra

learning style
Auditory, Visual
personality style
Grade Level
Middle School (6-8)
Lesson Type
Skill Sharpener

Lesson Plan - Get It!

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  • What do the numbers 1, 4, 9, 16, 25, and 36 all have in common?
  • What makes a perfect square?

What makes a square so special and perfect?

  • Squares are special shapes where all four sides are congruent, or have equal measure.
  • A perfect square is a number that has a square root that is a whole number.
  • A square root is when we find the number that, when multiplied by itself, equals the original number.
  • When the square root of a number is equal to a whole number, it is called a perfect square.
  • A number is a perfect square when you can take unit squares and form them into a larger square. A unit square is a square that has a length of 1 and a width of 1.

The first four perfect squares are 1, 4, 9, and 16, as shown below:

square root chart

  • Do you see how the multiplication fact relates to the square?

The number that multiplies by itself to create the perfect square, is also the length and width of the square.

  • What would be the fifth perfect square?
  • How would the square be drawn?
  • Discuss with a parent or teacher.

Perfect squares follow a sequence of numbers that increase by odd numbers. 1, 4, 9, 16, 25 are the first five perfect squares. Look at the diagram below:

diagram explaining square roots

Notice the sequence formed between the perfect squares.

  • If you follow that pattern, what would the next perfect square be?

The next odd number after 9 is 11, so 25 + 11 = 36. The square root of 36 is 6, so 36 is a perfect square.

  • What number would come next?

Take a look at an example of a number and determine if it is a perfect square:

chart explaining square root of 5

5 unit squares cannot be arranged to form a square. Remember that a square has a length and width that are the same measure. You can see in the two figures above that a square is not formed. Five is not a perfect square and its square root would be a decimal number.

Discuss with a parent or teacher how to determine if a number is a perfect square.

You can be better at math if you can quickly recall the first ten perfect squares. Listen to the Square Numbers Song, by Schoolbeatz, two times to practice the first ten perfect squares:

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Now that you have learned about what a perfect square is and how to identify a perfect square, you will practice with games and interactive practice in the Got It? section.

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