A square number, also referred to as a perfect square, is a type of figurate number (a number that can be represented using a regular geometric pattern formed using dots that are regularly spaced) formed by multiplying an integer by itself. Other examples of figurate numbers include triangular numbers and pentagonal numbers.
Square numbers are represented by an array with an equal number of rows and columns of regularly spaced dots. There are an equal number of dots on each side of the square and therefore an equal number of rows and columns in a square number. The number of dots is determined by the integer being squared (multiplied by itself). The result of squaring the integer is a square number, represented by the number of dots that form each square, as shown in the figure below.
The dots in red represent the integers being squared and the value in green below is the result of squaring the respective integers. A square number must be an integer. We can still square the number 1.5 to get 2.25, but 2.25 is not a square number because it is not an integer. There are many different methods for determining whether a number is a square number, but it can be helpful to know some of the smaller square numbers by heart, just like the multiplication table. Below is a table showing the first 20 square numbers:
|02 = 0||72 = 49||142 = 196|
|12 = 1||82 = 64||152 = 225|
|22 = 4||92 = 81||162 = 256|
|32 = 9||102 = 100||172 = 289|
|42 = 16||112 = 121||182 = 324|
|52 = 25||122 = 144||192 = 361|
|62 = 36||132 = 169||202 = 400|