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Last updated on June 3rd, 2025

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Cube of 686

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When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 686.

Cube of 686 for Australian Students
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Cube of 686

A cube number is a value obtained by raising a number to the power of 3, or by multiplying the number by itself three times. When you cube a positive number, the result is always positive. When you cube a negative number, the result is always negative. This is because a negative number multiplied by itself three times results in a negative number.

 

The cube of 686 can be written as 686³, which is the exponential form. Or it can also be written in arithmetic form as, 686 × 686 × 686.

 

cube of 686

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How to Calculate the Value of Cube of 686

In order to check whether a number is a cube number or not, we can use the following three methods: multiplication method, factor formula (a³), or by using a calculator. These three methods will help students to cube the numbers faster and easier without feeling confused or stuck while evaluating the answers.

 

  1. By Multiplication Method
  2. Using a Formula
  3. Using a Calculator
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By Multiplication Method

The multiplication method is a process in mathematics used to find the product of two numbers or quantities by combining them through repeated addition. It is a fundamental operation that forms the basis for more complex mathematical concepts.

 

Step 1: Write down the cube of the given number. 686³ = 686 × 686 × 686

 

Step 2: You get 322,486,432 as the answer. Hence, the cube of 686 is 322,486,432.

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Using a Formula (a³)

The formula (a + b)³ is a binomial formula for finding the cube of a number. The formula is expanded as a³ + 3a²b + 3ab² + b³.

 

Step 1: Split the number 686 into two parts. Let a = 680 and b = 6, so a + b = 686

 

Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³

 

Step 3: Calculate each term a³= 680³ 3a²b = 3 × 680² × 6 3ab² = 3 × 680 × 6² b³ = 6³

 

Step 4: Add all the terms together:

 

(a + b)³ = a³ + 3a²b + 3ab² + b³

 

(680 + 6)³= 680³ + 3 × 680² × 6 + 3 × 680 × 6² + 6³

 

686³ = 314,432,000 + 82,080 + 7,344 + 216

 

686³ = 322,486,432

 

Step 5: Hence, the cube of 686 is 322,486,432.

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Using a Calculator

To find the cube of 686 using a calculator, input the number 686 and use the cube function (if available) or multiply 686 × 686 × 686. This operation calculates the value of 686³, resulting in 322,486,432. It’s a quick way to determine the cube without manual computation.

 

Step 1: Ensure the calculator is functioning properly.

 

Step 2: Press 6 followed by 8 and 6

 

Step 3: If the calculator has a cube function, press it to calculate 686³.

 

Step 4: If there is no cube function on the calculator, simply multiply 686 three times manually.

 

Step 5: The calculator will display 322,486,432.

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Tips and Tricks for the Cube of 686

  • The cube of any even number is always even, while the cube of any odd number is always odd.

 

  • The product of two or more perfect cube numbers is always a perfect cube.

 

  • A perfect cube can always be expressed as the product of three identical groups of equal prime factors.
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Common Mistakes to Avoid When Calculating the Cube of 686

There are some typical errors that students might make during the process of cubing a number. Let us take a look at five of the major mistakes that students might make:

Mistake 1

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Incorrect Multiplication

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Students might multiply the numbers only twice. That is, 686 × 686 and not 686 × 686 × 686. Always remember that 686³ = 686 × 686 × 686.

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Solved Examples on Cube of 686

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Problem 1

What is the cube and cube root of 686?

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The cube of 686 is 322,486,432 and the cube root of 686 is approximately 8.807.

Explanation

First, let’s find the cube of 686.

 

We know that the cube of a number, such that x³ = y Where x is the given number, and y is the cubed value of that number

 

So, we get 686³ = 322,486,432

 

Next, we must find the cube root of 686

 

We know that the cube root of a number ‘x’ is x(1/3) Where x is the given number, and y is the cube root value of the number

 

So, we get 686(1/3) = 8.807

 

Hence, the cube of 686 is 322,486,432, and the cube root of 686 is approximately 8.807.

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Problem 2

If the side length of the cube is 686 cm, what is the volume?

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The volume is 322,486,432 cm³.

Explanation

Use the volume formula for a cube V = Side³. Substitute 686 for the side length: V = 686³ = 322,486,432 cm³.

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Problem 3

How much larger is 686³ than 680³?

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686³ – 680³ = 322,486,432 - 314,432,000 = 8,054,432.

Explanation

First find the cube of 686³, that is 322,486,432 Next, find the cube of 680³, which is 314,432,000 Now, find the difference between them using the subtraction method. 322,486,432 – 314,432,000 = 8,054,432 Therefore, 686³ is 8,054,432 larger than 680³.

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Problem 4

If a cube with a side length of 686 cm is compared to a cube with a side length of 300 cm, how much larger is the volume of the larger cube?

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The volume of the cube with a side length of 686 cm is 322,486,432 cm³

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).

 

Cubing 686 means multiplying 686 by itself three times: 686 × 686 = 470,596, and then 470,596 × 686 = 322,486,432.

 

The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.

 

Therefore, the volume of the cube is 322,486,432 cm³.

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Problem 5

Estimate the cube 685.9 using the cube 686.

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The cube of 685.9 is approximately 322,486,432.

Explanation

First, identify the cube of 686, The cube of 686 is 686³ = 322,486,432.

 

Since 685.9 is only a tiny bit less than 686, the cube of 685.9 will be almost the same as the cube of 686.

 

The cube of 685.9 is approximately 322,486,432 because the difference between 685.9 and 686 is very small.

 

So, we can approximate the value as 322,486,432.

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FAQs on Cube of 686

1.What are the perfect cubes up to 686?

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2.How do you calculate 686³?

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3.What is the meaning of 686³?

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4.What is the cube root of 686?

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5.Is 686 a perfect cube?

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6.How does learning Algebra help students in Australia make better decisions in daily life?

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7.How can cultural or local activities in Australia support learning Algebra topics such as Cube of 686?

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8.How do technology and digital tools in Australia support learning Algebra and Cube of 686?

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9.Does learning Algebra support future career opportunities for students in Australia?

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Important Glossaries for Cube of 686

  • Binomial Formula: It is an algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer raised to the base. The formula is used to find the square and cube of a number.

 

  • Cube of a Number: Multiplying a number by itself three times is called the cube of a number.

 

  • Exponential Form: It is a way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2 equals 8.

 

  • Volume of a Cube: The amount of space occupied by a cube, calculated as the cube of the side length, or side³.

 

  • Cube Root: The cube root of a number x is a value that, when multiplied by itself three times, gives the number x.
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About BrightChamps in Australia

At BrightChamps, algebra is much more than digits—it opens doors to unlimited possibilities! We are committed to helping kids all across Australia master important math skills, including today’s focus on the Cube of 686, with a special spotlight on cubes—in a fun, engaging, and easy-to-understand way. Whether your child is calculating the speed of a roller coaster at Luna Park Sydney, keeping score at a local cricket match, or managing their allowance for the latest gadgets, mastering algebra builds their confidence for daily life. Our interactive lessons make math learning simple and enjoyable. Because children in Australia learn in different ways, we adapt our approach to suit each child’s style. From Sydney’s vibrant streets to the beautiful beaches of the Gold Coast, BrightChamps brings algebra to life, making it exciting and relatable all over Australia. Let’s make cubes a fun part of every child’s math journey!
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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.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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