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Square Number Patterns

A square has all sides of the same length. The area of a square is the product of its width times its height, and for a square, these numbers are the same. So, any whole number which is a product of a number with itself is called a square number. For instance, 3 x 3 = 9 so 9 is a square number.

Not all numbers are square numbers, because we cannot find a whole number to multiply by itself to make 10, for example.

Here are some special square numbers. Use your calculator to find the first few then see if you can guess the pattern for the rest, checking your answers with the calculator again:

1 x 1
11 x 11
111 x 111
1111 x 1111
11111 x 11111
7 x 7
67 x 67
667 x 667
6667 x 6667
66667 x 66667
9 x 9
99 x 99
999 x 999
9999 x 9999
99999 x 99999
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Patterns