Square Numbers (original) (raw)

Last Updated : 23 Jul, 2025

**Square Numbers are the product of a number multiplied by itself. These are fundamental to mathematics. In this article, we will explain Square Numbers, Give Examples, List of Square Numbers from 1 to 100, Why are they called Square Numbers and others in detail.

Table of Content

• What is a Square Number?
• List of Square Numbers
• Perfect Square Numbers from 1 to 100
• Odd and Even Square Numbers
• List of Square Numbers (1 to 50)
• Properties of Square Numbers

What is a Square Number?

Square Numbers are numbers that are the square of an integer. It means any number that is square of a number is called a square number. Suppose we take a number 100 that is square of 10 then 100 is a square number. Mathematically, Square Number Definition is,

"Result of multiplying an integer by itself is an integer known as a square number. It is the product of multiplying a number by itself."

Square Numbers are always positive numbers. We know that,

****(+) × (+) = (+)**

****(-) × (-) = (+)**

For example, (-3)2 = 9.

Examples of Square Numbers

As we know, square numbers are those that result from multiplying an integer by itself. Here are some examples:

• 12 = 1
• 122 = 144
• 152 = 225
• 252 = 625
• 492 = 2401
• 812 = 6561

List of Square Numbers

List of all some square numbers are,

Square 1 to 30 Chart

Square 1 to 30 chart is added in form of image below,

Square Number in Geometry

Square shape in geometry has all its sides equal. Area of Square is equal to the square of its side.

Area of a Square = Side × Side = Side2

**Square Number = a × a = a 2

Formula of Square Number

Square of a Number is calculated using the formula,

Square Number of **n = n × n = n 2 (where "n" is an Integer)

**For example, Square of 3 = (3)2 = 9

Any real number may be squared using this formula, which just requires multiplying the number by itself.

Types of Square Numbers

Various square number types are,

• **One Digit Square Numbers: One digit numbers that are perfect square are called one digit square numbers. For example, 1, 4, 9 are one digit square numbers.
• **Two Digit Square Number: Two digit numbers that are perfect square are called two digit square numbers. For example, 16, 25, 36, etc. are two digit square numbers.
• **Three Digit Square Number: Three digit numbers that are perfect square are called three digit square numbers. For example, 121, 144, 169, etc. are three digit square numbers.

Apart, from these we can have Four Digit Square Numbers, Five Digit Square numbers, etc.

Perfect Square Numbers from 1 to 100

Integers with perfect square values between 1 and 100 can be written as the product of an integer times its own multiplication, yielding a whole number. Said another way, these figures represent the squares of whole numbers.

Since each number is expressed as the square of a certain integer, the list consists of

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

Odd and Even Square Numbers

• Square of odd numbers are always odd numbers.
• Square of even numbers are always even numbers.

**Odd Square Numbers: 1, 9, 25, 49, 81, ...

**Even Square Numbers: 4, 16, 36, 64, 100, ...

How to Calculate Squares of a Number?

To find calculate square of number multiply a number n by itself (n × n = n2). For example,

32 = 3 × 3 = 9

72 = 7 × 7 = 49

Using this method squares of any number is easily found,

List of Square Numbers (1 to 50)

Square Numbers of 1 to 50 is added in the table below,

Square Numbers from 51 to 100

Square from 51 and 100 are added in the table below,

Properties of Square Numbers

Various properties of square number are listed as follows:

**Square Numbers Symbol

• Symbol of Square is Superscript 2, such as n2

**Odd Square and Even Square

• Square of odd number is always an odd number, and square of even number is always an odd numbers. **Example: 42 = 16 (even), 32 = 9 (odd).
• **Sum of Consecutive Odd Numbers: Sum of first n odd numbers is equal to n2.
• **Square Roots: Square root of a square number are always integers. For example, √16 = 4

Why are They Called ‘Square’ Numbers?

Square numbers are square numbers because they are square of various integers, such as, **12 2 = 144 and ****(-9)** 2 = 81.

Square Roots

Square numbers are found when we multiply an integer is multiplied by itself. Square roots is opposite of this operation, squre roots are number which when multiplied by itself gives the original number.

**For example,

• 8 × 8 = 64
• √(64) = 8

We can say that, square root of any number is a number which when squared gets the original number.

**Read More,

• Perfect Cubes
• Square 1 to 30

Examples on Square Numbers 1 to 100

**Example 1: What is square of 8?

**Solution:

Square of 8 (82) is 64

**Example 2: Find square of 15.

**Solution:

Square of 15 (15)2 equals 225

**Example 3: What is square of 25?

**Solution:

Square of 25 is (25)2 is 625

**Example 4: Simplify 13 2 + 5 2 - 11 2

**Solution:

= 132 + 52 - 112

= 169 + 25 - 121

= 73

Practice Questions on Square Numbers

Some problems on square numbers are,

**Q1: Find the minimum number that must be subtracted from 8000 for the result to be a perfect square?

**Q2: If two consecutive perfect squares have a product that is a perfect square, find the two squares?

**Q3: Can a perfect square be created by adding two consecutive perfect cubes? If so, find it; if not, explain yourself?