Square of 1 to 100
2026-02-28 17:42 Diff
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Last updated on August 5, 2025

A square is the result obtained when a number is multiplied twice. For a number ‘x’, the square is x2. Square numbers are used in algebra, physics, for measuring the area of square-shaped objects, etc. In this topic, we will learn the squares from 1 to 100.

Square 1 to 100

The square of 1 to 100 ranges from 1 (12) to 100 (1002). Learning these squares is helpful when it comes to solving complex mathematical problems. The concept of squaring numbers comes from geometry, where we calculate the area of squares.

For example, squaring off 25 means multiplying 25 two times, which gives 625 → 25 × 25 = 625. Now let's find the squares of numbers from 1 to 100.

Square Numbers 1 to 100 Chart

Using the square numbers 1 to 100 chart, we can see how the square number is growing as we move from 1 to 100. Understanding these numbers will help you simply solve problems. Take a look at the chart given below.

List of all squares 1 to 100

This list will show you the list of squares from 12 to 1002. From the list of squares, we can understand how multiplying numbers by itself works. Here, we will look at the complete list of squares from 1 to 100.

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Square 1 to 100 - Even Numbers

Square numbers which can be divided by 2 are even square numbers. We get even square numbers when an even number gets multiplied by itself.

Given below is the list of even square numbers

Square 1 to 100 - Odd Numbers

Square numbers which cannot be divided by 2 are odd square numbers, Odd square numbers are obtained when an odd number is multiplied by itself.

Given below is the list of odd square numbers.

How to Calculate Square from 1 to 100

We write the square of a number as X2, where ‘X’ is multiplied by itself two times → X × X = X2. The two methods used to square the number are:

  • Multiplication Method
     
  • Expansion Method

Now let's discuss them in detail

Multiplication Method

Here, we simply multiply the number by itself to get the square. We can try finding the square of 45 according to the steps given:-

Step 1: To find the square of 45, apply the formula → X × X = X2.

Here, ‘X’ is 45

Step 2: Multiply 45 by itself → 45 × 45 = 2025

Hence, the square of 45 is 2025

We find the squares of 1 to 100 in this manner.

Expansion Method

This method helps in finding the square root of a number using an algebraic formula. Instead of directly multiplying the same number by itself, we use a formula to find the square. This rule helps in finding the square of numbers closer to numbers 10, 11, 12, and so on.

The formula is  (a + b)2 = a2 + 2ab + b2, where ‘a’ is the number closest to the number given and ‘b’ is the difference between the number given and ‘a’. 

Let’s find the square of 13 using the formula. Follow the steps given below:-

Step 1: We identify the value of ‘a’ as 12 and ‘b’ as 1. The value of ‘b’ is 1 because we multiplied 12 from the given number 13 → 13 - 12 = 1

Step 2: Now apply the value of ‘a’ and ‘b’ in the equation a2 + 2ab + b2
a2  = 144
2ab = 2 × 12 × 1 = 24
b2 = 1 × 1 = 1
a2 + 2ab + b2 = 144 + 24 + 1 = 169

So we find the square of 13 as 169

Rules for Calculating Squares 1 to 100

Rule 1: Multiplication Rule

The most basic rule to calculate squares is the multiplication rule. Here we multiply the number by itself two times to get the square. If a number is multiplied by another number, the result won’t be a square. For example, When 5 is multiplied by 5 we get 25 which is a square. Multiplying 5 by 6, we get 30 which is not a square.

Rule 2: Addition for Progressive Squares

The squares of the numbers are calculated by adding the consecutive odd numbers. Take the example of the first 8 numbers

12 =  1
22 = 1 + 3 = 4
32 = 1 + 3 + 5 = 9
42 = 1 + 3 + 5 + 7 = 16
52 = 1 + 3 + 5 + 7 + 9 = 25
62 = 1 + 3 + 5 + 7 + 9 + 11 = 36
72 = 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49
82 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64

Rule 3: Estimation of Large Numbers

For larger numbers, round them to the nearest simple numbers such as 10, 100, or 1000, then adjust the value. For example, to square 56, round it to 60 and adjust:
602 = 3600 

Then subtract the correction factor:

  • 3600−(2×60×4) + 42
     
  • 3600 - 480 + 16 = 3136

Thus, 562 = 56 × 56 = 3136

Tips and Tricks for Squares 1 to 100

For students to learn the squares from 1 to 100, here are a few tips and tricks. They will help you understand the squares easily.

Squaring numbers that end in 0

For numbers with the last digit as 0, multiply the non-zero part first and then add the remaining zeroes. For example, to find the squares of numbers 50 and 100, we multiply 5 by 5 and 1 by 1 first and then add the remaining zeroes.

  • 50 × 50 = 2500
     
  • 100 × 100 = 10000

Multiplication of Even Number

Multiplication of even numbers will always result in even perfect squares.
For example, the square of even numbers like 42, 84, 96 will always be even.

  • 42 × 42 = 1764
     
  • 84 × 84 = 7056
     
  • 96 × 96 = 9216

Multiplication of Odd Number

Multiplication of odd numbers will always result in odd perfect squares.
For example, the square of odd numbers like 31, 57, and 69 will always be odd

  • 31 × 31 = 961
     
  • 57 × 57 = 3249
     
  • 69 × 69 = 4761

Common Mistakes and How To Avoid Them in Squares 1 to 100

It’s common to make mistakes while learning about the squares. We will discuss some mistakes a child can make while finding the squares 1 to 100.

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Problem 1

Identify the perfect square from the list given below: 42, 3025, 420, 9025, 16, 139

Okay, lets begin

The perfect squares are 3025, 9025, and 16

Explanation

Squares are the products obtained when the same number gets multiplied by itself. The perfect squares from the list are 3025, 9025, and 16. These are the products obtained when 55, 95, and 4 get multiplied by itself.

55 × 55 = 3025

95 × 95 = 9025

4 × 4 = 16

Well explained 👍

Problem 2

Compare the squares and write which is greater. Is 7744 greater than 10000?

Okay, lets begin

No, 7744 is not greater than 10000

Explanation

The square root of the given perfect squares are 88 and 100. From this, we can say that 7744 is not greater but smaller than 10000

88 × 88 = 7744

100 × 100 = 10000

Well explained 👍

Problem 3

What will be the sum of two squares(45)² + (54)²?

Okay, lets begin

We will get the sum as 4941

Explanation

To find the sum, we need to find the squares of 45 and 54.

The squares of 45 and 54 are 2025 and 2916. Now add these numbers to get the sum of the perfect squares → 2025 + 2916 = 4941

Well explained 👍

FAQs on Squares 1 to 100

1.What is the sum of squares 9² and 81²?

We will get the sum as 6642.

The values for 92 and 812 are 81 and 6561.

Adding them we get 6642.

2.What will be the product of odd perfect squares 25 and 49?

We will get the product as 1225 → 25 × 49 = 1225

3.What is the square of 36?

The square of 36 is multiplying 36 by itself two times → 36 × 36 = 1296

4.Are all composite numbers perfect squares?

No, not all composite numbers are perfect squares. Composite numbers like 6, 8, 12, and so on are not perfect squares.

5.Is (-79)² a positive square?

Yes, (-79)2 is a positive square. Multiplying a negative number with a negative number results in a positive number. Therefore (-79)2 = (-79) x  (-79) = 6241.
 

Important Glossaries for Squares 1 to 100

  • Perfect Square: A number expressed as the square of an integer. For example, 400 is a perfect square when 20 is multiplied by itself.
  • Square Root: The opposite process of squaring a number. For example, √484 is 24.
  • Even Square: A number that results from multiplying an even number by itself. For example, 42 gives 16, 82 gives 64, 122 gives 144.
  • Square Chart: A visual representation of perfect square numbers.

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.