102 LearnersLast updated on May 26th, 2025
Square of 682
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 682.
What is the Square of 682
The square of a number is the product of the number itself. The square of 682 is 682 × 682. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 682², where 682 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 682 is 682 × 682 = 465,124.
Square of 682 in exponential form: 682²
Square of 682 in arithmetic form: 682 × 682
How to Calculate the Value of Square of 682
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 682.
Step 1: Identify the number. Here, the number is 682.
Step 2: Multiplying the number by itself, we get, 682 × 682 = 465,124.
The square of 682 is 465,124.
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 682.
So: 682² = 682 × 682 = 465,124.
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 682.
Step 1: Enter the number in the calculator Enter 682 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×) That is 682 × 682
Step 3: Press the equal to button to find the answer Here, the square of 682 is 465,124.
Tips and Tricks for the Square of 682
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 682
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.
Solved Examples on Square of 682
Problem 1
Find the side length of a square, where the area of the square is 465,124 cm².
The area of a square = a²
So, the area of a square = 465,124 cm²
So, the side length = √465,124 = 682.
The length of each side = 682 cm
Explanation
The side length of a square is 682 cm. Because the area is 465,124 cm², the length is √465,124 = 682.
Problem 2
Sarah is planning to tile her square patio of length 682 feet. The cost to tile a square foot is 5 dollars. Then how much will it cost to tile the full patio?
The length of the patio = 682 feet
The cost to tile 1 square foot of the patio = 5 dollars.
To find the total cost to tile, we find the area of the patio,
Area of the patio = area of the square = a²
Here a = 682
Therefore, the area of the patio = 682² = 682 × 682 = 465,124.
The cost to tile the patio = 465,124 × 5 = 2,325,620.
The total cost = 2,325,620 dollars
Explanation
To find the cost to tile the patio, we multiply the area of the patio by the cost to tile per foot. So, the total cost is 2,325,620 dollars.
Problem 3
Find the area of a circle whose radius is 682 meters.
The area of the circle = 1,463,778.72 m²
Explanation
The area of a circle = πr²
Here, r = 682
Therefore, the area of the circle = π × 682²
= 3.14 × 682 × 682
= 1,463,778.72 m².
Problem 4
The area of the square is 465,124 cm². Find the perimeter of the square.
The perimeter of the square is 2,728 cm.
Explanation
The area of the square = a²
Here, the area is 465,124 cm²
The length of the side is √465,124 = 682
Perimeter of the square = 4a
Here, a = 682
Therefore, the perimeter = 4 × 682 = 2,728 cm.
Problem 5
Find the square of 683.
The square of 683 is 466,489.
Explanation
The square of 683 is multiplying 683 by 683. So, the square = 683 × 683 = 466,489.
FAQs on Square of 682
1.What is the square of 682?
2.What is the square root of 682?
3.Is 682 a prime number?
4.What are the first few multiples of 682?
5.What is the square of 681?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square of 682?
8.How do technology and digital tools in India support learning Algebra and Square of 682?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for Square 682.
- Perfect square: A number that is the square of an integer, such as 1, 4, 9, 16, etc.
- Exponent: A mathematical notation indicating the number of times a number is multiplied by itself, such as in 5².
- Square root: The square root is the value that, when multiplied by itself, gives the original number, like √144 = 12.
- Multiplication: The process of combining equal groups to find the total number of items, such as in 7 × 8 = 56.
- Calculator: A device or software used to perform arithmetic operations, such as finding the square of numbers.
Explore More algebra
Previous to Square of 682
About BrightChamps in India
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.
