What Is a List of Perfect Squares?

By Staff WriterLast Updated Apr 4, 2020 5:43:03 AM ET
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A list of perfect squares under 100 includes 1, 4, 9, 16, 25, 36, 49, 64 and 81. Perfect squares are infinite in number because they are found by multiplying a number by itself, meaning that the possibilities are endless. Although there are many square numbers, perfect squares are unique and very easy to calculate since whole numbers are involved.


An example of a perfect square is 144. This number is the result of 12 squared, or the multiplication of 12 times 12, so finding the square of the figure is performing the reverse equation. In this case, 144 can be divided by 12 to give the same answer of 12. Just as subtraction is the inverse of addition and division is the inverse of multiplication, discovering the square root is the opposite of squaring.

Perfect squares are rare due to the requirement of a number having to be squared. Every number can be squared, but most do not result in a whole number. For example, 18 is not a perfect square because the square root of this number is a decimal between 4 and 5. The square root for this number can be found, but the process is far more complicated than working with perfect squares. Often, a calculator is used for finding the square root of numbers that are not perfect squares.