132 LearnersLast updated on May 29th, 2025
Square of 321
The product of multiplying an integer by itself is the square of a number. Square is used in programming, calculating areas, and so on. In this topic, we will discuss the square of 321.
What is the Square of 321
The square of a number is the product of the number itself.
The square of 321 is 321 × 321.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 321², where 321 is the base and 2 is the exponent.
The square of a positive and a negative number is always positive. For example, 5² = 25; -5² = 25.
The square of 321 is 321 × 321 = 103041.
Square of 321 in exponential form: 321²
Square of 321 in arithmetic form: 321 × 321
How to Calculate the Value of Square of 321
The square of a number is multiplying the number by itself. So let’s learn how to find the square of a number. These are the common methods used to find the square of a number.
- By Multiplication Method
- Using a Formula (a2)
- Using a Calculator
By the Multiplication method
In this method, we will multiply the number by itself to find the square. The product here is the square of the number. Let’s find the square of 321.
Step 1: Identify the number. Here, the number is 321.
Step 2: Multiplying the number by itself, we get, 321 × 321 = 103041.
The square of 321 is 103041.
Using a Formula (a²)
In this method, the formula a² is used to find the square of the number, where a is the number.
Step 1: Understanding the equation Square of a number = a²
a² = a × a
Step 2: Identifying the number and substituting the value in the equation.
Here, ‘a’ is 321
So: 321² = 321 × 321 = 103041
By Using a Calculator
Using a calculator to find the square of a number is the easiest method. Let’s learn how to use a calculator to find the square of 321.
Step 1: Enter the number in the calculator. Enter 321 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 321 × 321
Step 3: Press the equal to button to find the answer. Here, the square of 321 is 103041.
Tips and Tricks for the Square of 321
Tips and tricks make it easy for students to understand and learn the square of a number. To master the square of a number, these tips and tricks will help students.
- The square of an even number is always an even number. For example, 6² = 36.
- The square of an odd number is always an odd number. For example, 5² = 25.
- The last digit of the square of a number is always 0, 1, 4, 5, 6, or 9.
- If the square root of a number is a fraction or a decimal, then the number is not a perfect square. For example, √1.44 = 1.2.
- The square root of a perfect square is always a whole number. For example, √144 = 12.
Common Mistakes to Avoid When Calculating the Square of 321
Mistakes are common among kids when doing math, especially when it is finding the square of a number. Let’s learn some common mistakes to master the squaring of a number.
Mistake 1
Calculation errors:
Calculation errors mostly happen when students skip the steps or else by swapping the digits. To avoid it, students should double-check the answer. They can double-check by finding the square root of the solution they found.
For example, the square of 25 is 625, and the square root of 625 is ±25.
Mistake 2
Errors will be using the formula.
The formula to find the square of the number is a². Instead, students may use 321² with (3+2+1)² or (300+20+1)². So students should check and use the correct formula and double-check the answers to avoid all the confusion.
Mistake 3
Confusing with square and square root.
Not understanding the concept of square and square root can lead to confusion in students. To avoid it, students should understand the concept that square and square root are inverse operations. The square of 5 is 25 and the square root of 25 is ±5.
Mistake 4
Errors in parentheses.
Ignoring the parentheses when finding the square of a number can lead to errors. So, students should understand parentheses. And do the operations in the correct order to avoid error.
Mistake 5
Not practicing regularly.
Regular practice is required to master the square of a number. So students should do regular practice to avoid errors.
Solved Examples on Square of 321
Problem 1
Find the length of the square, where the area of the square is 103041 cm².
The area of a square = a²
So, the area of a square = 103041 cm²
So, the length = √103041 = 321.
The length of each side = 321 cm
Explanation
The length of a square is 321 cm.
Because the area is 103041 cm², the length is √103041 = 321.
Problem 2
Anna is planning to decorate her square garden of length 321 feet. The cost to decorate a foot is 5 dollars. Then how much will it cost to decorate the full garden?
The length of the garden = 321 feet
The cost to decorate 1 square foot of garden = 5 dollars.
To find the total cost to decorate, we find the area of the garden.
Area of the garden = area of the square = a²
Here a = 321
Therefore, the area of the garden = 321² = 321 × 321 = 103041.
The cost to decorate the garden = 103041 × 5 = 515205.
The total cost = 515205 dollars
Explanation
To find the cost to decorate the garden, we multiply the area of the garden by the cost to decorate per foot. So, the total cost is 515205 dollars.
Problem 3
Find the area of a circle whose radius is 321 meters.
The area of the circle = 323,686.17 m²
Explanation
The area of a circle = πr²
Here, r = 321
Therefore, the area of the circle = π × 321² = 3.14 × 321 × 321 = 323,686.17 m².
Problem 4
The area of the square is 103041 cm². Find the perimeter of the square.
The perimeter of the square is 1284 cm
Explanation
The area of the square = a²
Here, the area is 103041 cm²
The length of the side is √103041 = 321
Perimeter of the square = 4a
Here, a = 321
Therefore, the perimeter = 4 × 321 = 1284 cm.
Problem 5
Find the square of 322.
The square of 322 is 103684
Explanation
The square of 322 is multiplying 322 by 322.
So, the square = 322 × 322 = 103684
FAQs on Square of 321
1.What is the square of 321?
2.What is the square root of 321?
3.Is 321 a prime number?
4.What are the first few multiples of 321?
5.What is the square of 320?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square of 321?
8.How do technology and digital tools in Australia support learning Algebra and Square of 321?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Square 321.
- Square: The result of multiplying a number by itself.
- Exponent: The power to which a number is raised, indicating how many times to multiply the base by itself.
- Perfect Square: A number that is the square of an integer.
- Prime Number: A number greater than 1 that has no positive divisors other than 1 and itself.
- Multiplication: An arithmetic operation that combines two quantities to find their product.
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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.
