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102 LearnersLast updated on October 9, 2025
Square 20 to 100
The square of a number is the multiplication of a number ‘N’ by itself. Square numbers are used practically in situations like finding the area of a garden or measuring distance on maps. In this topic, we are going to learn about the square numbers from 20 to 100.
Square 20 to 100
Numbers 20 to 100, when squared, give values ranging from 400 to 10,000. Squaring numbers can be useful for solving complex math problems.
For example, squaring the number 25 implies multiplying the number twice. So that means 25 × 25 = 625. So let us look into the square numbers from 20 to 100.
Square Numbers 20 to 100 Chart
Learning square numbers helps us find the area of two-dimensional shapes like squares. Let’s take a look at the chart of square numbers from 20 to 100 given below.
Understanding these values helps in various math concepts like measuring areas and so on. Let’s dive into the chart of squares.
List of All Squares 20 to 100
We will be listing the squares of numbers from 20 to 100. Squares are an interesting part of math that help us solve various problems easily. Let’s take a look at the complete list of squares from 20 to 100.
Square 20 to 100 — Even Numbers Square numbers that are divisible by 2 are even. The square of any even number will result in an even number. Let’s look at the even numbers in the squares of 20 to 100.
Square 20 to 100 — Odd Numbers When you multiply an odd number by itself, the result is also an odd number. When we square an odd number, the result will always be odd.
Let’s look at the odd numbers in the squares of 20 to 100.
How to Calculate Squares From 20 to 100
The square of a number is written as N², which means multiplying the number N by itself. We use the formula given below to find the square of any number: N² = N × N
Let’s explore two methods to calculate squares: the multiplication method and the expansion method:
Multiplication method: In this method, we multiply the given number by itself to find the square of the number. Take the given number, for example, let’s take 24 as N. Multiply the number by itself: N² = 24 × 24 = 576 So, the square of 24 is 576. You can repeat the process for all numbers from 20 to 100.
Expansion method: In this method, we use algebraic formulas to break down the numbers for calculating easily. We use this method for larger numbers. Using the formula: (ab)² = a² + 2ab + b² For example: Find the square of 84. 84² = (80 + 4)²
To expand this, we use the algebraic identity (a + b)²= a² + 2ab + b². Here, a = 80 and b = 4. = 80² + 2 × 80 × 4 + 4² 80² = 6400; 2 × 80 × 4 = 640; 4² = 16 Now, adding them together: 6400 + 640 + 16 = 7056 So, the square of 84 is 7056.
Rules for Calculating Squares 20 to 100
When learning how to calculate squares, there are a few rules that we need to follow. These rules will help guide you through the process of calculating squares.
Rule 1: Multiplication Rule
The basic rule of squaring a number is to multiply the number by itself. We use the formula given below, to find the square of numbers: N² = N × N For example, 92 = 9 × 9 = 81.
Rule 2: Addition of progressive squares
In the addition of progressive squares, we calculate square numbers by adding consecutive odd numbers. For example, 1² = 1 → 1 (only the first odd number) 2² = 4 → 1 + 3 = 4 3² = 9 → 1 + 3 + 5 = 9 4² = 16 → 1 + 3 + 5 + 7 = 16 5² = 25 → 1 + 3 + 5 + 7 + 9 = 25.
Rule 3: Estimation for large numbers
For larger numbers, round them to the nearest simple number, then adjust the value. For example, to square 98, round it to 100 and adjust: 100² = 10,000, then subtract the correction factor 10,000 - (2 × 100 × 2) + 2² 10,000 - 400 + 4 = 9604 Thus, 98² = 9604.
Tips and Tricks for Squares 20 to 100
To make learning squares easier for kids, here are a few tips and tricks that can help you quickly find the squares of numbers from 20 to 100. These tricks will help you understand squares easily. Square numbers follow a pattern in unit place
- Square numbers end with these numbers in the one digit 0, 1, 4, 5, 6, or 9.
- If the last digit of a number is 2, 3, 7, or 8, it cannot be a square number. For example, 64 is a square number that ends with 4, while 81 is also a square number that ends with 1.
- Even or Odd property The square of an even number will always be even, and the square of an odd number will always be odd. For example, the square of 6 is 36, which is even. And the square of 7 is 49, which is odd.
- Adding odd numbers Square numbers can be calculated by adding the odd numbers one after the other. For example, 1² = 1 → 1 (only the first odd number) 2² = 4 → 1 + 3 = 4 3² = 9 → 1 + 3 + 5 = 9 4² = 16 → 1 + 3 + 5 + 7 = 16 5² = 25 → 1 + 3 + 5 + 7 + 9 = 25.
Common Mistakes and How to Avoid Them in Squares 20 to 100
When learning about squares, it’s natural to make some mistakes along the way. Let’s explore some common mistakes children often make and how you can avoid them. This will help get a better understanding of squares.
Mistake 1
Confusing squaring as doubling
Children think that squaring a number is the same as doubling it. For example, 25² is 625, not 50. Always remember that squaring means multiplying the number by itself.
Mistake 2
Confusing square and square root
Kids assume that squaring and square rooting are the same. For example, they might think that √81 equals 81², whereas they are not.
Squaring increases the value, while the square root finds the original number.
Mistake 3
Improperly squaring a negative number
Kids assume that the square of a negative number is negative. For example, instead of writing (-9)² as 81, they write it as -81.
Always remember that the square of a negative number is positive.
Mistake 4
Assuming all composite numbers as perfect squares
Kids assume that all composite numbers are perfect squares.
For example, numbers like 45, 60, and 90 are composite but not perfect squares.
Mistake 5
Using the wrong formula for squares
Students sometimes apply incorrect formulas. For example, the formula for squares is N², meaning N × N, but they confuse it with 2N, which is multiplying the number N by 2, not squaring it.
We must make sure we understand the difference and apply the correct formula.
Square 20 to 100 Examples
Problem 1
Find the square of 35.
The square of 35 is 1225. 35² = 35 × 35 = 1225
Explanation
We can break down 35 × 35 as: 35 × 35 = (30 + 5) × (30 + 5)
To expand this, we use the algebraic identity (a + b)²= a² + 2ab + b².
Here, a = 30 and b = 5. = 30² + 2 × 30 × 5 + 5² 30² = 900; 2 × 30 × 5 = 300; 5² = 25
Now, adding them together: 900 + 300 + 25 = 1225
So, the square of 35 is 1225.
Problem 2
Find the square of 72.
The square of 72 is 5184. 72² = 72 × 72 = 5184
Explanation
We can break down 72 × 72 as: 72 × 72 = (70 + 2) × (70 + 2)
To expand this, we use the algebraic identity (a + b)² = a² + 2ab + b².
Here, a = 70 and b = 2. =70² + 2 × 70 × 2 + 2² =4900 + 280 + 4 =5184.
Problem 3
Find the square of 100.
The square of 100 is 10,000. 100² = 100 × 100 = 10,000
Explanation
Since 100 × 100 is a simple multiplication, we directly get the answer: 100 × 100 = 10,000.
Thus, the square of 100 is 10,000.
Problem 4
Observe the pattern in square numbers: 20², 21², 22²,... 30². Find the pattern in their differences.
The differences follow an odd-number sequence: 41, 43, 45, 47, ... This shows that square numbers increase by consecutive odd numbers.
Explanation
Calculating the squares: 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900
Now, finding the differences: 441 − 400 = 41, 484 − 441 = 43, 529 − 484 = 45, 576 − 529 = 47,...
Problem 5
Is 72 a perfect square?
72 is not a perfect square.
Explanation
Perfect squares are numbers that result from squaring whole numbers.
If a number lies between two square values, it is not a perfect square.
Find the closest squares: 8² = 64, 9² = 81
Since 72 is not equal to any square of a whole number, it is not a perfect square.
FAQs on Squares 20 to 100
1.What are the odd perfect square numbers from 20 to 100?
2.Are all square numbers positive?
3.What is the sum of the perfect squares from 20 to 100?
4.What is the square of 50?
5.Are all prime numbers perfect squares?
Important Glossaries for Squares 20 to 100
- Odd square number: A square number that we get from squaring an odd number. For example, 81 is 9², which is an odd square number.
- Even square number: A square number that we get from squaring an even number. For example, 64 is 8², which is an even square number.
- Perfect square: A number that can be expressed as a product of a number when multiplied by itself. For example, 64 is a perfect square as 8 × 8 = 64.
- Multiplication method: A method to find the square of a number by multiplying the number by itself.
- Expansion method: A method to find the square of a number using algebraic identities to simplify the calculation.
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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.
