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103 LearnersLast updated on September 28, 2025
Square 100 to 300
A square of a number is the multiplication of a number ‘N’ by itself two times. 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 100 to 300.
Square 100 to 300
Numbers 100 to 300, when squared, give values ranging from 10,000 to 90,000. Squaring numbers can be useful for solving complex math problems.
For example, squaring the number 12 implies multiplying the number twice. So that means 12 × 12 = 144. So let us look into the square numbers from 100 to 300.
Square Numbers 100 to 300 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 100 to 300 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 100 to 300
We will be listing the squares of numbers from 100 to 300. Squares are an interesting part of math, that helps us solve various problems easily. Let’s take a look at the complete list of squares from 100 to 300.
Square 100 to 300 — 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 100 to 300.
Square 100 to 300 — 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 100 to 300.
How to Calculate Squares From 100 to 300
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 14 as N. Multiply the number by itself: N² = 14 × 14 = 196 So, the square of 14 is 196. You can repeat the process for all numbers from 100 to 300.
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 112. 112² = (110 + 2)² To expand this, we use the algebraic identity (a + b)² = a² + 2ab + b². Here, a = 110 and b = 2. = 110² + 2 × 110 × 2 + 2² 110² = 12100; 2 × 110 × 2 = 440; 2² = 4 Now, adding them together: 12100 + 440 + 4 = 12544 So, the square of 112 is 12544.
Rules for Calculating Squares 100 to 300
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, 122 = 12 × 12 = 144.
Rule 2: Addition of progressive squares
In the addition of progressive squares, we calculate square numbers by adding consecutive odd numbers. For example, 13² = 169 → 1 + 3 + 5 + 7 + ... + 25 = 169
Rule 3: Estimation for large numbers
For larger numbers, round them to the nearest simple number, then adjust the value. For example, to square 298, round it to 300 and adjust: 300² = 90000, then subtract the correction factor 90000 - (2 × 300 × 2) + 2² 90000 - 1200 + 4 = 88904 Thus, 298² = 88904.
Tips and Tricks for Squares 100 to 300
To make learning squares easier for students, here are a few tips and tricks that can help you quickly find the squares of numbers from 100 to 300. 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, 225 is a square number that ends with 5, while 196 is also a square number that ends with 6.
- 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 12 is 144 which is even. And the square of 13 is 169 which is odd.
- Adding odd numbers Square numbers can be calculated by adding the odd numbers one after the other. For example, 13² = 169 → 1 + 3 + 5 + 7 + ... + 25 = 169
Common Mistakes and How to Avoid Them in Squares 100 to 300
When learning about squares, it’s natural to make some mistakes along the way. Let’s explore some common mistakes students often make and how you can avoid them. This will help get a better understanding of squares.
Mistake 1
Confusing squaring as doubling
Students think that squaring a number is the same as doubling it.
For example, 12² is 144 not 24. Always remember that squaring means multiplying the number by itself.
Mistake 2
Confusing square and square root
Students 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
Students assume that the square of a negative number is negative.
For example, instead of writing (-10)² as 100 they write it as -100. Always remember that the square of a negative number is positive.
Mistake 4
Assuming all composite numbers as perfect squares
Students assume that all composite numbers are perfect squares.
For example, numbers like 198, 200, and 243 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 with 2, not squaring it.
We must make sure we understand the difference and apply the correct formula.
Square 100 to 300 Examples
Problem 1
Find the square of 213.
The square of 213 is 45369. 213² = 213 × 213 = 45369
Explanation
We can break down 213 × 213 as: 213 × 213 = (210 + 3) × (210 + 3)
To expand this, we use the algebraic identity (a + b)² = a² + 2ab + b².
Here, a = 210 and b = 3. = 210² + 2 × 210 × 3 + 3² 210² = 44100; 2 × 210 × 3 = 1260; 3² = 9
Now, adding them together: 44100 + 1260 + 9 = 45369
So, the square of 213 is 45369.
Problem 2
Find the square of 275.
The square of 275 is 75625. 275² = 275 × 275 = 75625
Explanation
We can break down 275 × 275 as: 275 × 275 = (280 - 5) × (280 - 5)
To expand this, we use the algebraic identity (a - b)² = a² - 2ab + b².
Here, a = 280 and b = 5. = 280² - 2 × 280 × 5 + 5² = 78400 - 2800 + 25 = 75625.
Problem 3
Find the square of 300.
The square of 300 is 90000. 300² = 300 × 300 = 90000
Explanation
Since 300 × 300 is a simple multiplication, we directly get the answer: 300 × 300 = 90000.
Thus, the square of 300 is 90000.
Problem 4
Observe the pattern in square numbers: 102, 112, 122,…202. Find the pattern in their differences.
The differences follow an odd-number sequence: 21, 23, 25, 27,… This shows that square numbers increase by consecutive odd numbers.
Explanation
Calculating the squares: 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400
Now, finding the differences: 121 − 100 = 21, 144 − 121 = 23, 169 − 144 = 25, 196 − 169 = 27,…
Problem 5
Is 180 a perfect square?
180 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: 13² = 169, 14² = 196 Since 180 is not equal to any square of a whole number, it is not a perfect square.
FAQs on Squares 100 to 300
1.What are the odd perfect square numbers up to 300?
2.Are all square numbers positive?
3.What is the sum of the perfect squares up to the number 300?
4.What is the square of 150?
5.Are all prime numbers perfect squares?
Important Glossaries for Squares 100 to 300
- Odd square number: A square number that we get from squaring an odd number. For example, 169 is a square of 13, which is an odd number.
- Even square number: A square number that we get from squaring an even number. For example, 196 is a square of 14, which is an even number.
- Perfect square: The number which can be expressed as a product of a number when multiplied by itself. For example, 225 is a perfect square as 15 × 15 = 225
- Algebraic identity: A formula used to simplify the squaring of numbers, such as (a + b)² = a² + 2ab + b².
- Composite number: A number that has more than two factors. For example, 180 is composite but not a perfect square.
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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.
