Cube of 684
2026-02-21 20:27 Diff
https://brightchamps.com/en-us/math/algebra/cube-of-684

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Last updated on August 5, 2025

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

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.

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

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.

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.

Tips and Tricks for the Cube of 684

  • 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.

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:

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Problem 1

What is the cube and cube root of 684?

Okay, lets begin

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.

Well explained 👍

Problem 2

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

Okay, lets begin

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.

Well explained 👍

Problem 3

How much larger is 684³ than 600³?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 5

Estimate the cube of 683 using the cube of 684.

Okay, lets begin

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.

Well explained 👍

FAQs on Cube of 684

1.What are the perfect cubes up to 684?

The perfect cubes up to 684 are 1, 8, 27, 64, 125, 216, 343, and 512.

2.How do you calculate 684³?

To calculate 684³, use the multiplication method, 684 × 684 × 684, which equals 319,018,464.

3.What is the meaning of 684³?

684³ means 684 multiplied by itself three times, or 684 × 684 × 684.

4.What is the cube root of 684?

5.Is 684 a perfect cube?

No, 684 is not a perfect cube because no integer multiplied by itself three times equals 684.

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