119 LearnersLast updated on May 26th, 2025
Square of 686
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 the topic, we will discuss the square of 686.
What is the Square of 686
The square of a number is the product of the number itself. The square of 686 is 686 × 686. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 686², where 686 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 686 is 686 × 686 = 470596.
Square of 686 in exponential form: 686²
Square of 686 in arithmetic form: 686 × 686
How to Calculate the Value of Square of 686
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 686.
Step 1: Identify the number. Here, the number is 686.
Step 2: Multiplying the number by itself, we get, 686 × 686 = 470596.
The square of 686 is 470596.
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 686
So: 686² = 686 × 686 = 470596
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 686.
Step 1: Enter the number in the calculator Enter 686 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×) That is 686 × 686
Step 3: Press the equal to button to find the answer Here, the square of 686 is 470596.
Tips and Tricks for the Square of 686
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 686
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 686² with (6+8+6)² or (600+80+6)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 686
Problem 1
Find the length of the square, where the area of the square is 470596 cm².
The area of a square = a²
So, the area of a square = 470596 cm²
So, the length = √470596 = 686.
The length of each side = 686 cm
Explanation
The length of a square is 686 cm. Because the area is 470596 cm² the length is √470596 = 686.
Problem 2
Sarah is planning to tile her square garden of length 686 feet. The cost to tile a foot is 5 dollars. Then how much will it cost to tile the full garden?
The length of the garden = 686 feet
The cost to tile 1 square foot of garden = 5 dollars.
To find the total cost to tile, we find the area of the garden,
Area of the garden = area of the square = a²
Here a = 686
Therefore, the area of the garden = 686² = 686 × 686 = 470596.
The cost to tile the garden = 470596 × 5 = 2352980.
The total cost = 2352980 dollars
Explanation
To find the cost to tile the garden, we multiply the area of the garden by the cost to tile per foot. So, the total cost is 2352980 dollars.
Problem 3
Find the area of a circle whose radius is 686 meters.
The area of the circle = 1,479,236.64 m²
Explanation
The area of a circle = πr²
Here, r = 686
Therefore, the area of the circle = π × 686²
= 3.14 × 686 × 686
= 1,479,236.64 m².
Problem 4
The area of the square is 470596 cm². Find the perimeter of the square.
The perimeter of the square is 2744 cm.
Explanation
The area of the square = a²
Here, the area is 470596 cm²
The length of the side is √470596 = 686
Perimeter of the square = 4a
Here, a = 686
Therefore, the perimeter = 4 × 686 = 2744.
Problem 5
Find the square of 687.
The square of 687 is 471969
Explanation
The square of 687 is multiplying 687 by 687. So, the square = 687 × 687 = 471969
FAQs on Square of 686
1.What is the square of 686?
2.What is the square root of 686?
3.Is 686 a composite number?
4.What are the first few multiples of 686?
5.What is the square of 685?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square of 686?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square of 686?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for Square of 686.
- Composite number: A number that has more than two factors, meaning it can be divided by numbers other than 1 and itself. For example, 4, 6, 8, 9, etc.
- 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.
- Even number: An integer divisible by 2 without a remainder. For example, 2, 4, 6, 8, etc.
- Perfect square: A number that is the square of an integer. For example, 1, 4, 9, 16, etc.
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About BrightChamps in United Arab Emirates
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.
