117 LearnersLast updated on May 26th, 2025
Square of 680
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 680.
What is the Square of 680
The square of a number is the product of the number itself. The square of 680 is 680 × 680. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 680², where 680 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 680 is 680 × 680 = 462,400.
Square of 680 in exponential form: 680²
Square of 680 in arithmetic form: 680 × 680
How to Calculate the Value of Square of 680
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 680.
Step 1: Identify the number. Here, the number is 680.
Step 2: Multiplying the number by itself, we get, 680 × 680 = 462,400.
The square of 680 is 462,400.
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 680.
So: 680² = 680 × 680 = 462,400
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 680.
Step 1: Enter the number in the calculator Enter 680 in the calculator.
Step 2: Multiply the number by itself using the multiplication button(×) That is 680 × 680
Step 3: Press the equal to button to find the answer Here, the square of 680 is 462,400.
Tips and Tricks for the Square of 680
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 680
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 680² with (6+8+0)² or (600+80)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 680
Problem 1
Find the length of the square, where the area of the square is 462,400 cm².
The area of a square = a²
So, the area of a square = 462,400 cm²
So, the length = √462,400 = 680.
The length of each side = 680 cm
Explanation
The length of a square is 680 cm. Because the area is 462,400 cm² the length is √462,400 = 680.
Problem 2
Sarah is planning to paint her square wall of length 680 feet. The cost to paint a foot is 5 dollars. Then how much will it cost to paint the full wall?
The length of the wall = 680 feet
The cost to paint 1 square foot of wall = 5 dollars.
To find the total cost to paint, we find the area of the wall,
Area of the wall = area of the square = a²
Here a = 680
Therefore, the area of the wall = 680² = 680 × 680 = 462,400.
The cost to paint the wall = 462,400 × 5 = 2,312,000.
The total cost = 2,312,000 dollars
Explanation
To find the cost to paint the wall, we multiply the area of the wall by cost to paint per foot. So, the total cost is 2,312,000 dollars.
Problem 3
Find the area of a circle whose radius is 680 meters.
The area of the circle = 1,453,287.04 m²
Explanation
The area of a circle = πr²
Here, r = 680
Therefore, the area of the circle = π × 680²
= 3.14 × 680 × 680
= 1,453,287.04 m².
Problem 4
The area of the square is 462,400 cm². Find the perimeter of the square.
The perimeter of the square is 2,720 cm.
Explanation
The area of the square = a²
Here, the area is 462,400 cm²
The length of the side is √462,400 = 680
Perimeter of the square = 4a
Here, a = 680
Therefore, the perimeter = 4 × 680 = 2,720.
Problem 5
Find the square of 681.
The square of 681 is 463,761.
Explanation
The square of 681 is multiplying 681 by 681. So, the square = 681 × 681 = 463,761.
FAQs on Square of 680
1.What is the square of 680?
2.What is the square root of 680?
3.Is 680 an even number?
4.What are the first few multiples of 680?
5.What is the square of 679?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square of 680?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square of 680?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for Square of 680.
- Even number: An even number is any integer that is exactly divisible by 2. For example, 2, 4, 6, 8.
- Exponential form: Exponential form is the way of writing a number in the form of a power. For example, 9² where 9 is the base and 2 is the power.
- Square root: The square root is the inverse operation of the square. The square root of a number is a number whose square is the number itself.
- Perfect square: A perfect square is a number that can be expressed as the square of an integer. For example, 16 is a perfect square because it is 4².
- Multiples: Multiples of a number are the products of that number with integers. For example, multiples of 3 are 3, 6, 9, 12.
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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
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