What is a Perfect Square?
A perfect square is found by taking a whole number and squaring it, or multiplying it by itself.
Let's create a list of the first 25 perfect squares:
Let's create a list of the first 25 perfect squares:
These numbers are perfect squares because they actually make a square as shown in the image below:
You should begin to familiarize yourself with this list so you can quickly identify perfect squares. Ideally, you should "memorize" and be able to recognize at least the first 15 perfect squares.
Watch the video below for another demonstration on identifying perfect squares.
Watch the video below for another demonstration on identifying perfect squares.
Perfect Squares by SmithMathAcademy: https://www.youtube.com/watch?v=pordwxv5HZE
Practice:
Use the following website to practice identifying perfect squares:
(scroll down to the bottom and choose "new problem" to get started)
http://www.onemathematicalcat.org/algebra_book/online_problems/is_num_perfect_square.htm
(scroll down to the bottom and choose "new problem" to get started)
http://www.onemathematicalcat.org/algebra_book/online_problems/is_num_perfect_square.htm
Perfect Squares with Variables
Now that you can identify perfect squares, we are going to add another piece to the puzzle. Perfect squares can also include variables. Using the product of powers property (see Properties of Exponents Review), when you multiply two variables together, you add the exponents. Therefore,
are perfect squares. Additionally, you can multiply a perfect square from your list above with a variable that is a perfect square - the result is also a perfect square. Some examples are listed below:
When you have become a master at identifying perfect squares, go back and retake the pre-test. You should score 80% or higher before moving on.
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