Properties of Square Numbers

Properties of Square Numbers are explained with examples here. The square numbers are the numbers that are produced when a number is multiplied to itself (Check: Square Numbers). For example, 4 is a square number that is produced when 2 is multiplied by itself. It is expressed as:

2² = 4 [Two squared equals four]

In this article, we will discuss the different properties of square numbers. But before we proceed with the properties, let’s have a look at square numbers from 1 to 50.

Square Numbers 1 to 50

Here is the list of square numbers from 1 to 50, where N is the natural number and N² is the square of N. The list will help us to learn about the properties of square numbers.

What are the Properties of Square Numbers?

As we have already seen the list of squares from 1 to 50 from the above section, the following properties of square numbers can be generalised:

• Square numbers end with 0, 1, 4, 5, 6 or 9 at the unit’s place
• If a number ends with 1 or 9, then its square will always end with 1
• If a number ends with 4 or 6, then its square will always end with 6
• Unit digit of square of any number will be the unit digit of square of its last digit
• The square root of perfect square is always a natural number
• The perfect squares will end with even numbers of zeros
• Square of even numbers are always even
• Square of odd numbers are always odd

Let us discuss all these properties of square numbers with examples.

Square numbers end with 0, 1, 4, 5, 6 or 9

If we check the squares of numbers from 1 to 10, the unit digit of the square numbers will have 0, 1, 4, 5, 6 or 9. Thus, for all the perfect squares, the unit digit will consist of only 0, 1, 4, 5, 6 or 9 and none of the square numbers will end with 2, 3, 7 or 8.

Square of Numbers ending with 1 or 9 always end with 1

According to this property, if the number ends with 1 or 9, then the square of the number always ends with 1 at the unit place. See some examples below:

Square of Numbers ending with 4 or 6 always end with 6

As per this property of square numbers, if a number ends with 4 or 6 at the unit’s place, then the square of that number will always end with 6 at the unit place. The examples are:

Unit digit of square of number is the same as unit digit of square of its last digit

This property explains the square of any number such as a two-digit number will have the same digit at unit place, as the square of its unit digit will have.

For example, the square of 23 is 529

23² = 529

The unit place of 23 has 3 and unit place of 529 has 9

Square of 3 is equal to 9

Square root of perfect square is always a natural number

Examples of perfect squares are 4, 9, 16, 25, etc.

Hence, if we take the square root of these perfect squares, we will get a natural number only.

Therefore, square root is the inverse method of finding the square of a number.

Perfect squares will end with even numbers of zeros

If a number ends with zero at unit place, then the square of such a number will always end with even numbers of zeros. See the example below to understand this property.

Square of even numbers are always even

As per the property, the square of even numbers will always result in an even number. Thus,

(2n)² = 4n²

Where n is any natural number.

Square of odd numbers are always odd

If we find the square of any odd number, the result will always be an odd number. Thus,

(2n + 1)² = 4(n² + n) + 1

Where n is any natural number

Squares and Square Root Related Articles

• Square and Square Root
• Square Root 1 to 100
• Square Root Of A Number By Repeated Subtraction
• Square Root And Cube Root
• Square Root Questions
• Sum of Squares
• How to Find Square Root

Video Lesson on Numbers