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Last updated on June 2nd, 2025

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Cube of 684

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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 the cube of 684.

Cube of 684 for Singaporean Students
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Cube of 684

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 by itself three times results in a negative number.

 

The cube of 684 can be written as 684³, which is the exponential form. Or it can also be written in arithmetic form as, 684 × 684 × 684.

 

cube of 684

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How to Calculate the Value of Cube of 684

In order to check whether a number is a cube number or not, we can use the following three methods, such as multiplication method, a factor formula (a³), or by using a calculator. These three methods will help kids 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. 684³ = 684 × 684 × 684

 

Step 2: You get 319,018,464 as the answer. Hence, the cube of 684 is 319,018,464.

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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 684 into two parts, as 600 and 84. Let a = 600 and b = 84, so a + b = 684

 

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

 

Step 3: Calculate each term

 

a³ = 600³

 

3a²b = 3 × 600² × 84

 

3ab² = 3 × 600 × 84²

 

b³ = 84³

 

Step 4: Add all the terms together:

 

(a + b)³ = a³ + 3a²b + 3ab² + b³

 

(600 + 84)³ = 600³ + 3 × 600² × 84 + 3 × 600 × 84² + 84³

 

684³ = 216,000,000 + 90,720,000 + 25,401,600 + 5,896,864

 

684³ = 319,018,464

 

Step 5: Hence, the cube of 684 is 319,018,464.

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Using a Calculator

To find the cube of 684 using a calculator, input the number 684 and use the cube function (if available) or multiply 684 × 684 × 684. This operation calculates the value of 684³, resulting in 319,018,464. It’s a quick way to determine the cube without manual computation.

 

Step 1: Ensure the calculator is functioning properly.

 

Step 2: Enter 684

 

Step 3: If the calculator has a cube function, press it to calculate 684³.

 

Step 4: If there is no cube function on the calculator, simply multiply 684 three times manually.

 

Step 5: The calculator will display 319,018,464.

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Tips and Tricks for the Cube of 684

  • 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 684

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

Mistake 1

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Incorrect Multiplication

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Kids might multiply the numbers only twice. That is, 684 × 684 and not 684 × 684 × 684. Always remember that 684³ = 684 × 684 × 684.

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Solved Examples on Cube of 684

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Problem 1

What is the cube and cube root of 684?

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The cube of 684 is 319,018,464 and the cube root of 684 is approximately 8.826.

Explanation

First, let’s find the cube of 684.

 

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

 

So, we get 684³ = 319,018,464

 

Next, we must find the cube root of 684 We know that the cube root of a number ‘x’ is such that ∛x = y Where ‘x’ is the given number, and y is the cube root value of the number

 

So, we get ∛684 ≈ 8.826

 

Hence the cube of 684 is 319,018,464 and the cube root of 684 is approximately 8.826.

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Problem 2

If the side length of a cube is 684 cm, what is the volume?

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The volume is 319,018,464 cm³.

Explanation

Use the volume formula for a cube V = Side³.

 

Substitute 684 for the side length: V = 684³ = 319,018,464 cm³.

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Problem 3

How much larger is 684³ than 600³?

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684³ – 600³ = 103,018,464.

Explanation

First, find the cube of 684, which is 319,018,464

 

Next, find the cube of 600, which is 216,000,000

 

Now, find the difference between them using the subtraction method. 319,018,464 – 216,000,000 = 103,018,464

 

Therefore, 684³ is 103,018,464 larger than 600³.

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Problem 4

If a cube with a side length of 684 cm is compared to a cube with a side length of 84 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 684 cm is 313,121,600 cm³ larger.

Explanation

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

 

Cubing 684 means multiplying 684 by itself three times: 684 × 684 × 684 = 319,018,464.

 

Cubing 84 means multiplying 84 by itself three times: 84 × 84 × 84 = 5,896,864.

 

Now, subtract the volume of the smaller cube from the larger cube: 319,018,464 – 5,896,864 = 313,121,600 cm³.

 

Therefore, the volume of the cube with a side length of 684 cm is 313,121,600 cm³ larger than the one with 84 cm.

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Problem 5

Estimate the cube of 683 using the cube of 684.

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The cube of 683 is approximately 319,018,464.

Explanation

First, identify the cube of 684, The cube of 684 is 684³ = 319,018,464.

 

Since 683 is only a tiny bit less than 684, the cube of 683 will be almost the same as the cube of 684.

 

The cube of 683 is approximately 319,018,464 because the difference between 683 and 684 is very small.

 

So, we can approximate the value as 319,018,464.

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FAQs on Cube of 684

1.What are the perfect cubes up to 684?

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2.How do you calculate 684³?

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3.What is the meaning of 684³?

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4.What is the cube root of 684?

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5.Is 684 a perfect cube?

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

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7.How can cultural or local activities in Singapore support learning Algebra topics such as Cube of 684?

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8.How do technology and digital tools in Singapore support learning Algebra and Cube of 684?

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

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Important Glossaries for Cube of 684

  • 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 space occupied by a cube, calculated as the cube of its side length.

 

  • Perfect Cube: A number that can be expressed as the cube of an integer.
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About BrightChamps in Singapore

At BrightChamps, algebra is more than just digits—it opens doors to countless possibilities! We are passionate about supporting kids all across Singapore in mastering vital math skills, like today’s focus on the Cube of 684, with a special focus on cubes—in a lively, easy-to-understand, and enjoyable way. Whether your child is figuring out how fast a roller coaster moves at Universal Studios Singapore, tracking scores at local football matches, or managing their allowance for the newest gadgets, mastering algebra builds their confidence in everyday life. Our interactive lessons make math fun and approachable. Since kids in Singapore learn differently, we customize our teaching to suit each learner’s style. From the city’s bustling streets to its beautiful gardens, BrightChamps brings algebra to life, making it exciting and meaningful across Singapore. 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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