Cube of 84
2026-02-28 17:45 Diff
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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 while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 84.

Cube of 84

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 84 can be written as 84³, which is the exponential form.

Or it can also be written in arithmetic form as, 84 × 84 × 84.

How to Calculate the Value of Cube of 84

In order to check whether a number is a cube number or not, we can use the following three methods: 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.

  • By Multiplication Method
     
  • Using a Formula (a3)
     
  • 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. 84³ = 84 × 84 × 84

Step 2: You get 592,704 as the answer.

Hence, the cube of 84 is 592,704.

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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 84 into two parts, such as 80 and 4. Let a = 80 and b = 4, so a + b = 84

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

Step 3: Calculate each term a³ = 80³ 3a²b = 3 × 80² × 4 3ab² = 3 × 80 × 4² b³ = 4³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (80 + 4)³ = 80³ + 3 × 80² × 4 + 3 × 80 × 4² + 4³ 84³ = 512,000 + 76,800 + 3,840 + 64 84³ = 592,704

Step 5: Hence, the cube of 84 is 592,704.

Using a Calculator

To find the cube of 84 using a calculator, input the number 84 and use the cube function (if available) or multiply 84 × 84 × 84. This operation calculates the value of 84³, resulting in 592,704. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 8 followed by 4

Step 3: If the calculator has a cube function, press it to calculate 84³.

Step 4: If there is no cube function on the calculator, simply multiply 84 three times manually.

Step 5: The calculator will display 592,704.

Tips and Tricks for the Cube of 84

  • 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.

Common Mistakes to Avoid When Calculating the Cube of 84

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 84?

Okay, lets begin

The cube of 84 is 592,704 and the cube root of 84 is approximately 4.396.

Explanation

First, let’s find the cube of 84.

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 84³ = 592,704 Next, we must find the cube root of 84

We know that the cube root of a number x, such that ³√x = y

Where x is the given number, and y is the cube root value of the number

So, we get ³√84 ≈ 4.396

Hence the cube of 84 is 592,704 and the cube root of 84 is approximately 4.396.

Well explained 👍

Problem 2

If the side length of the cube is 84 cm, what is the volume?

Okay, lets begin

The volume is 592,704 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 84 for the side length: V = 84³ = 592,704 cm³.

Well explained 👍

Problem 3

How much larger is 84³ than 74³?

Okay, lets begin

84³ – 74³ = 286,776.

Explanation

First find the cube of 84³, which is 592,704

Next, find the cube of 74³, which is 305,928

Now, find the difference between them using the subtraction method. 592,704 – 305,928 = 286,776

Therefore, the 84³ is 286,776 larger than 74³.

Well explained 👍

Problem 4

If a cube with a side length of 84 cm is compared to a cube with a side length of 24 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 84 cm is 592,704 cm³

Explanation

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

Cubing 84 means multiplying 84 by itself three times: 84 × 84 = 7,056, and then 7,056 × 84 = 592,704.

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

Therefore, the volume of the cube is 592,704 cm³.

Well explained 👍

Problem 5

Estimate the cube 83.9 using the cube 84.

Okay, lets begin

The cube of 83.9 is approximately 592,704.

Explanation

First, identify the cube of 84,

The cube of 84 is 84³ = 592,704. Since 83.9 is only a tiny bit less than 84, the cube of 83.9 will be almost the same as the cube of 84.

The cube of 83.9 is approximately 592,704 because the difference between 83.9 and 84 is very small.

So, we can approximate the value as 592,704.

Well explained 👍

FAQs on Cube of 84

1.What are the perfect cubes up to 84?

The perfect cubes up to 84 are 1, 8, 27, and 64.

2.How do you calculate 84³?

To calculate 84³, use the multiplication method, 84 × 84 × 84, which equals 592,704.

3.What is the meaning of 84³?

84³ means 84 multiplied by itself three times, or 84 × 84 × 84.

4.What is the cube root of 84?

5.Is 84 a perfect cube?

No, 84 is not a perfect cube because no integer multiplied by itself three times equals 84.

Important Glossaries for Cube of 84

  • 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, which equals 8.
  • Perfect Cube: A number that can be expressed as the product of an integer multiplied by itself three times.
  • Volume of a Cube: The amount of space inside a cube, calculated as the side length raised to the power of three.

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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

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