Square Numbers: Understanding the Concept and Properties

What is a square number?

When it comes to learning mathematics, one of the fundamental concepts is understanding what a square number is. Square numbers are essential for many mathematical operations, and they are used in various fields, including science and engineering.

A square number is the result of multiplying a number by itself.

For example, 3 multiplied by 3 equals 9 , making 9 a square number.

Square numbers are used in algebra, geometry, and even in everyday life. They are essential for calculating areas and volumes, and they are used in many scientific calculations. Understanding square numbers is the foundation of many mathematical operations, and it is essential for anyone who wants to excel in maths.

Definition And Explanation

In mathematics, a square number is the product of a whole number multiplied by itself.

For example, 9 is a square number because it is the product of 3 multiplied by 3 . The symbol for square is ², so 3^2 is equal to 9 .

Square numbers have an integer as their square root. In other words, the square root of a square number is a whole number.

\sqrt{9} = 3

Properties of Square Numbers

There are several properties of square numbers that are useful to know:

  • Square numbers are always non-negative. This means they are greater than or equal to zero.
  • The product of two square numbers is also a square number. For example, 4 \times 9 = 36 , which is a square number.
  • The square of an even number is always an even number, and the square of an odd number is always an odd number.


Let’s look at some examples of square numbers. Square numbers are the result of multiplying an integer by itself. For example, 3 \times 3 = 9 , so 9 is a square number.

Here are the first 10 square numbers:

  • 1 \times 1 = 1
  • 2 \times 2 = 4
  • 4 \times 4 = 16
  • 5 \times 5 = 25
  • 6 \times 6 = 36
  • 7 \times 7 = 49
  • 8 \times 8 = 64
  • 9 \times 9 = 81
  • 10 \times 10 = 100

Square numbers are often used in mathematics, even in algebraic concepts such as the difference of two squares , and other fields. For example, in geometry, the area of a square is the square of its side length. If a square has a side length of 5 units, its area is 5 \times 5 = 25 square units.


After exploring what square numbers are, you have learned that they are numbers that are obtained by multiplying an integer by itself. We have also discovered that square numbers can be arranged to fill a perfect square, hence the name square numbers.

You have seen that square numbers have several properties, such as being non-negative, and that they can be represented as the sum of consecutive odd numbers. You have also learned that square numbers play an important role in mathematics, particularly in geometry and algebra.

Overall, understanding what square numbers are and their properties can help us solve mathematical problems more efficiently and accurately. By recognising square numbers, we can simplify calculations and make connections between different mathematical concepts.