Cube of 820
2026-02-28 10:22 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 when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 820.

Cube of 820

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 820 can be written as 820³, which is the exponential form. Or it can also be written in arithmetic form as, 820 × 820 × 820.

How to Calculate the Value of Cube of 820

In order to check whether a number is a cube number or not, we can use the following three methods, such as the 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. 820³ = 820 × 820 × 820

Step 2: You get 551,368,000 as the answer. Hence, the cube of 820 is 551,368,000.

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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 820 into two parts, as 800 and 20. Let a = 800 and b = 20, so a + b = 820

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

Step 3: Calculate each term

a³ = 800³

3a²b = 3 × 800² × 20

3ab² = 3 × 800 × 20²

b³ = 20³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(800 + 20)³ = 800³ + 3 × 800² × 20 + 3 × 800 × 20² + 20³

820³ = 512,000,000 + 384,000,000 + 96,000 + 8,000

820³ = 551,368,000

Step 5: Hence, the cube of 820 is 551,368,000.

Using a Calculator

To find the cube of 820 using a calculator, input the number 820 and use the cube function (if available) or multiply 820 × 820 × 820. This operation calculates the value of 820³, resulting in 551,368,000. 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 2 followed by 0

Step 3: If the calculator has a cube function, press it to calculate 820³.

Step 4: If there is no cube function on the calculator, simply multiply 820 three times manually.

Step 5: The calculator will display 551,368,000.

Tips and Tricks for the Cube of 820

  • 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 820

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 820?

Okay, lets begin

The cube of 820 is 551,368,000 and the cube root of 820 is approximately 9.434.

Explanation

First, let’s find the cube of 820.

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 820³ = 551,368,000

Next, we must find the cube root of 820 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 ∛820 ≈ 9.434

Hence the cube of 820 is 551,368,000 and the cube root of 820 is approximately 9.434.

Well explained 👍

Problem 2

If the side length of the cube is 820 cm, what is the volume?

Okay, lets begin

The volume is 551,368,000 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 820 for the side length: V = 820³ = 551,368,000 cm³.

Well explained 👍

Problem 3

How much larger is 820³ than 810³?

Okay, lets begin

820³ – 810³ = 24,552,000.

Explanation

First, find the cube of 820³, that is 551,368,000

Next, find the cube of 810³, which is 526,816,000

Now, find the difference between them using the subtraction method. 551,368,000 – 526,816,000 = 24,552,000

Therefore, 820³ is 24,552,000 larger than 810³.

Well explained 👍

Problem 4

If a cube with a side length of 820 cm is compared to a cube with a side length of 200 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 820 cm is 551,368,000 cm³

Explanation

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

Cubing 820 means multiplying 820 by itself three times: 820 × 820 = 672,400, and then 672,400 × 820 = 551,368,000.

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

Therefore, the volume of the cube is 551,368,000 cm³.

Well explained 👍

Problem 5

Estimate the cube of 819.9 using the cube of 820.

Okay, lets begin

The cube of 819.9 is approximately 551,368,000.

Explanation

First, identify the cube of 820, The cube of 820 is 820³ = 551,368,000.

Since 819.9 is only a tiny bit less than 820, the cube of 819.9 will be almost the same as the cube of 820.

The cube of 819.9 is approximately 551,368,000 because the difference between 819.9 and 820 is very small.

So, we can approximate the value as 551,368,000.

Well explained 👍

FAQs on Cube of 820

1.What are the perfect cubes up to 820?

The perfect cubes up to 820 include numbers like 1, 8, 27, 64, 125, 216, 343, 512, and 729.

2.How do you calculate 820³?

To calculate 820³, use the multiplication method, 820 × 820 × 820, which equals 551,368,000.

3.What is the meaning of 820³?

820³ means 820 multiplied by itself three times, or 820 × 820 × 820.

4.What is the cube root of 820?

5.Is 820 a perfect cube?

No, 820 is not a perfect cube because no integer multiplied by itself three times equals 820.

Important Glossaries for Cube of 820

  • 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: The amount of space that a substance or object occupies, or that is enclosed within a container, especially when great. It is often measured in cubic units.
  • Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For 820, the cube root is approximately 9.434.

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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.