Square numbers and their properties. A square number is a number that can be expressed as the product of two equal integers.

For example, 4 is a square number because it can be expressed as 2 x 2.

## Properties of Square Numbers

Square numbers are always positive: Since square numbers are the product of two equal integers, they are always positive.

Square numbers can be represented as dots in the shape of a square: For example, the square number 4 can be represented as a square of 2×2 dots.

Square numbers are a subset of the perfect squares: A perfect square is a number that can be expressed as the product of an integer and itself. For example, 16 is a perfect square because it can be expressed as 4 x 4. All square numbers are perfect squares, but not all perfect squares are square numbers.

## Examples of Square Numbers

- 1 is a square number because it can be expressed as 1 x 1.
- 4 is a square number because it can be expressed as 2 x 2.
- 9 is a square number because it can be expressed as 3 x 3.
- 16 is a square number because it can be expressed as 4 x 4.
- 25 is a square number because it can be expressed as 5 x 5.
- 36 is a square number because it can be expressed as 6 x 6.

Finding Square Numbers To find the square of a number, we multiply the number by itself. For example, to find the square of 3, we multiply 3 by 3, which gives us 9. So, 9 is the square of 3.

We can also find square numbers by squaring integers. For example, we can find the square of 7 by squaring the integer 7, which gives us 49.

Application of Square Numbers Square numbers have many applications in mathematics, science, and engineering. For example, they are used in the calculation of areas of squares and in determining the distance between two points in coordinate geometry.

Practice Exercise Now that you have learned about square numbers and their properties, let’s try a practice exercise.

- Identify the square numbers between 1 and 20.
- Find the square of 8.
- Is 27 a square number?

## Answers:

- 1, 4, 9, 16
- 64
- No, 27 is not a square number.

Square numbers are an important concept in mathematics that have many applications. They are numbers that can be expressed as the product of two equal integers and have many interesting properties. Square numbers, you can improve your problem-solving skills and gain a better understanding of mathematical concepts.