Cube of 840
2026-02-28 00:46 Diff
https://brightchamps.com/en-us/math/algebra/cube-of-840

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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 840.

Cube of 840

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 840 can be written as 840³, which is the exponential form. Or it can also be written in arithmetic form as, 840 × 840 × 840.

How to Calculate the Value of Cube of 840

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 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. 840³ = 840 × 840 × 840

Step 2: You get 592,704,000 as the answer. Hence, the cube of 840 is 592,704,000.

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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 840 into two parts, as 800 and 40. Let a = 800 and b = 40, so a + b = 840

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

Step 3: Calculate each term

a³ = 800³

3a²b = 3 × 800² × 40

3ab² = 3 × 800 × 40²

b³ = 40³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(800 + 40)³ = 800³ + 3 × 800² × 40 + 3 × 800 × 40² + 40³

840³ = 512,000,000 + 76,800,000 + 38,400,000 + 64,000

840³ = 592,704,000

Step 5: Hence, the cube of 840 is 592,704,000.

Using a Calculator

To find the cube of 840 using a calculator, input the number 840 and use the cube function (if available) or multiply 840 × 840 × 840. This operation calculates the value of 840³, resulting in 592,704,000. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Input 840

Step 3: If the calculator has a cube function, press it to calculate 840³.

Step 4: If there is no cube function on the calculator, simply multiply 840 three times manually.

Step 5: The calculator will display 592,704,000.

Tips and Tricks for the Cube of 840

  • 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 840

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

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Problem 1

What is the cube and cube root of 840?

Okay, lets begin

The cube of 840 is 592,704,000 and the cube root of 840 is approximately 9.434.

Explanation

First, let’s find the cube of 840.

We know that 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 840³ = 592,704,000

Next, we must find the cube root of 840 We know that cube root of a number ‘x’, such that ∛x = y Where x is the given number, and y is the cube root value of the number

So, we get ∛840 ≈ 9.434

Hence, the cube of 840 is 592,704,000 and the cube root of 840 is approximately 9.434.

Well explained 👍

Problem 2

If the side length of the cube is 840 cm, what is the volume?

Okay, lets begin

The volume is 592,704,000 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 840 for the side length: V = 840³ = 592,704,000 cm³.

Well explained 👍

Problem 3

How much larger is 840³ than 740³?

Okay, lets begin

840³ – 740³ = 326,496,000.

Explanation

First, find the cube of 840³, which is 592,704,000.

Next, find the cube of 740³, which is 266,208,000.

Now, find the difference between them using the subtraction method. 592,704,000 – 266,208,000 = 326,496,000

Therefore, the 840³ is 326,496,000 larger than 740³.

Well explained 👍

Problem 4

If a cube with a side length of 840 cm is compared to a cube with a side length of 10 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 840 cm is 592,704,000 cm³.

Explanation

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

Cubing 840 means multiplying 840 by itself three times: 840 × 840 = 705,600, and then 705,600 × 840 = 592,704,000.

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

Therefore, the volume of the cube is 592,704,000 cm³.

Well explained 👍

Problem 5

Estimate the cube of 839.5 using the cube of 840.

Okay, lets begin

The cube of 839.5 is approximately 592,704,000.

Explanation

First, identify the cube of 840, The cube of 840 is 840³ = 592,704,000.

Since 839.5 is very close to 840, the cube of 839.5 will be almost the same as the cube of 840.

The cube of 839.5 is approximately 592,704,000 because the difference between 839.5 and 840 is very small.

So, we can approximate the value as 592,704,000.

Well explained 👍

FAQs on Cube of 840

1.What are the perfect cubes up to 840?

The perfect cubes up to 840 are 1, 8, 27, 64, 125, 216, 343, 512, and 729.

2.How do you calculate 840³?

To calculate 840³, use the multiplication method, 840 × 840 × 840, which equals 592,704,000.

3.What is the meaning of 840³?

840³ means 840 multiplied by itself three times, or 840 × 840 × 840.

4.What is the cube root of 840?

5.Is 840 a perfect cube?

No, 840 is not a perfect cube because no integer multiplied by itself three times equals 840.

Important Glossaries for Cube of 840

  • 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.
  • Cube Root: The number which, when multiplied by itself three times, gives the original number.
  • Volume of a Cube: The amount of space occupied by a cube, calculated using the formula V = Side³, where 'Side' is the length of a side of the cube.

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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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