118 LearnersLast updated on May 26th, 2025
Square of 684
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 684.
What is the Square of 684
The square of a number is the product of the number itself. The square of 684 is 684 × 684. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 684², where 684 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 684 is 684 × 684 = 467,856.
Square of 684 in exponential form: 684²
Square of 684 in arithmetic form: 684 × 684
How to Calculate the Value of Square of 684
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
- 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 684.
Step 1: Identify the number. Here, the number is 684.
Step 2: Multiplying the number by itself, we get, 684 × 684 = 467,856.
The square of 684 is 467,856.
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 684.
So: 684² = 684 × 684 = 467,856
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 684.
Step 1: Enter the number in the calculator. Enter 684 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 684 × 684.
Step 3: Press the equal to button to find the answer. Here, the square of 684 is 467,856.
Tips and Tricks for the Square of 684
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 684
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 swap 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 when using the formula.
The formula to find the square of the number is a². Instead, students may use 684² with (6 + 8 + 4)² or (600 + 80 + 4)². So students should check and use the correct formula and double-check the answers to avoid all the confusion.
Mistake 3
Confusing 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 errors.
Mistake 5
Not practicing regularly.
Regular practice is required to master the square of a number. So students should practice regularly to avoid errors.
Solved Examples on Square of 684
Problem 1
Find the length of a square, where the area of the square is 467,856 cm².
The area of a square = a²
So, the area of a square = 467,856 cm²
So, the length = √467,856 = 684.
The length of each side = 684 cm
Explanation
The length of a square is 684 cm. Because the area is 467,856 cm², the length is √467,856 = 684.
Problem 2
Lisa is planning to tile her square floor with a length of 684 feet. The cost to tile a foot is 5 dollars. Then how much will it cost to tile the entire floor?
The length of the floor = 684 feet
The cost to tile 1 square foot of the floor = is 5 dollars.
To find the total cost to tile, we find the area of the floor,
Area of the floor = area of the square = a²
Here a = 684
Therefore, the area of the floor = 684² = 684 × 684 = 467,856.
The cost to tile the floor = 467,856 × 5 = 2,339,280.
The total cost = 2,339,280 dollars
Explanation
To find the cost to tile the floor, we multiply the area of the floor by the cost to tile per foot. So, the total cost is 2,339,280 dollars.
Problem 3
Find the area of a circle whose radius is 684 meters.
The area of the circle = 1,470,265.44 m²
Explanation
The area of a circle = πr²
Here, r = 684
Therefore, the area of the circle = π × 684²
= 3.14 × 684 × 684
= 1,470,265.44 m².
Problem 4
The area of a square is 467,856 cm². Find the perimeter of the square.
The perimeter of the square is 2,736 cm.
Explanation
The area of the square = a²
Here, the area is 467,856 cm²
The length of the side is √467,856 = 684
Perimeter of the square = 4a Here, a = 684
Therefore, the perimeter = 4 × 684 = 2,736.
Problem 5
Find the square of 685.
The square of 685 is 469,225.
Explanation
The square of 685 is multiplying 685 by 685. So, the square = 685 × 685 = 469,225.
FAQs on Square of 684
1.What is the square of 684?
2.What is the square root of 684?
3.Is 684 a prime number?
4.What are the first few multiples of 684?
5.What is the square of 683?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square of 684?
8.How do technology and digital tools in United States support learning Algebra and Square of 684?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Square 684
- Perfect square: A number that is the square of an integer. For example, 144 is a perfect square because it is 12².
- Exponent: The number that indicates how many times the base is multiplied by itself. For example, in 684², 2 is the exponent.
- Square root: The value that, when multiplied by itself, gives the original number. For example, the square root of 144 is 12.
- Whole number: A number without fractions; an integer.
- Multiplication: The arithmetic operation of combining groups of equal sizes. For example, multiplying 684 by 684.
Explore More algebra
![Important Math Links Icon]()
Previous to Square of 684
About BrightChamps in United States
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.
