 # 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.

 N N2 N N2 N N2 N N2 N N2 1 1 11 121 21 441 31 961 41 1681 2 4 12 144 22 484 32 1024 42 1764 3 9 13 169 23 529 33 1089 43 1849 4 16 14 196 24 576 34 1156 44 1936 5 25 15 225 25 625 35 1225 45 2025 6 36 16 256 26 676 36 1296 46 2116 7 49 17 289 27 729 37 1369 47 2209 8 64 18 324 28 784 38 1444 48 2304 9 81 19 361 29 841 39 1521 49 2401 10 100 20 400 30 900 40 1600 50 2500

## 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.

 Examples: 12 = 1 22 = 4 32 = 9 42 = 16 52 = 25 62 = 36 72 = 49 82 = 64 92 = 81 102 = 100

### 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:

 Examples: 112 = 121 212 = 441 192 = 361 292 = 841

### 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:

 142 = 196 162 = 256 242 = 576

### 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.

 √4 = 2 √9 = 3 √16 = 4 √25 = 5

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.

 Examples: 102 = 100 202 = 400 502 = 2500 1002 = 10000 7002 = 4900

### 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.

 Examples: 22 = 4 62 = 36 122 = 144 182 = 324 302 = 900

### 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

 Examples: 72 = 49 152 = 225 232 = 529 452 = 2025

## Frequently Asked Questions on Properties of Square Numbers

### What are the four properties of square numbers?

Square numbers always end with digits 0, 1, 4, 5, 6 or 9, at its unit place. Square of a number ending with 4 and 6, will always end with 6 at unit place. If a number has 1 or 9 in the unit’s place, then it’s square ends in 1. Square numbers can only have an even number of zeros at the end.

### What is the square of number 35?

The square number of 35 is 1225.

### What is the property of square of even numbers?

The square of even numbers are always even numbers.

### What is the property of a square of odd numbers?

The square of odd numbers are always odd numbers.

### Is 49 a perfect square or not?

49 is a perfect square because the root of 49 is equal to 7.