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Square numbers are numbers that are the results (products) of multiplying the same number twice. Just as we have repeated addition for multiplication, square numbers are repeated multiplication of the same number (integer) twice.

The number of times a number multiplies itself is referred to as its powers or exponent. So with square numbers,they raised to the power of 2; if ‘n’ is an integer (natural number), then n x n = n squared = m (square number)

A natural number is the same as the whole or the usual counting numbers {0, 1, 2, 3, 4, 5, 6, 7, 8,...}.

When dealing with square numbers, we hear of perfect squares. What then is it? A perfect square is the square of a natural number.

For example, 64 is a perfect square because 8 x 8 = 82 = 64.

Working out square numbers can be easy enough. It’s all about knowing the times tables. We can understand that a square number is the the product of a number multiplied by itself.

A look at the multiplication grid below shows all the the perfect squares from 1 to 144. The numbers highlighted and forming a diagonal are the ones that can be spotted on the grid. They are found where a number from a column and the same number from a row meet.

So 1 x 1 = 12= 1, 6 x 6 = 62= 36, and 11 x 11 = 112 = 121.

Multiplication grid with perfect squares

Perfect squares

Shall we now consider the basic concepts of square numbers.


The perfect squares of all natural numbers end with 1, 4, 9, 6, 5 and 0 at its units place.

The table below shows some examples.


The squares of all odd numbers end with 1, 5, or 9.