Cube of 842
2026-02-28 01:36 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 842.

Cube of 842

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 842 can be written as 842³, which is the exponential form. Or it can also be written in arithmetic form as 842 × 842 × 842.

How to Calculate the Value of Cube of 842

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 methods help to cube numbers faster and easier without confusion or feeling 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 numbers 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. 842³ = 842 × 842 × 842

Step 2: You get 596,516,648 as the answer. Hence, the cube of 842 is 596,516,648.

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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 842 into two parts, as 800 and 42. Let a = 800 and b = 42, so a + b = 842

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

Step 3: Calculate each term

a³ = 800³

3a²b = 3 × 800² × 42

3ab² = 3 × 800 × 42²

b³ = 42³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(800 + 42)³ = 800³ + 3 × 800² × 42 + 3 × 800 × 42² + 42³

842³ = 512,000,000 + 80,640,000 + 42,336,000 + 74,088

842³ = 596,516,648

Step 5: Hence, the cube of 842 is 596,516,648.

Using a Calculator

To find the cube of 842 using a calculator, input the number 842 and use the cube function (if available) or multiply 842 × 842 × 842. This operation calculates the value of 842³, resulting in 596,516,648. 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 and then 2

Step 3: If the calculator has a cube function, press it to calculate 842³.

Step 4: If there is no cube function on the calculator, simply multiply 842 three times manually.

Step 5: The calculator will display 596,516,648.

Tips and Tricks for the Cube of 842

  • 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 842

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:

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Problem 1

What is the cube and cube root of 842?

Okay, lets begin

The cube of 842 is 596,516,648, and the cube root of 842 is approximately 9.430.

Explanation

First, let’s find the cube of 842.

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 842³ = 596,516,648

Next, we must find the cube root of 842

We know that the 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 ∛842 ≈ 9.430

Hence, the cube of 842 is 596,516,648, and the cube root of 842 is approximately 9.430.

Well explained 👍

Problem 2

If the side length of the cube is 842 cm, what is the volume?

Okay, lets begin

The volume is 596,516,648 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 842 for the side length: V = 842³ = 596,516,648 cm³.

Well explained 👍

Problem 3

How much larger is 842³ than 800³?

Okay, lets begin

842³ – 800³ = 84,516,648.

Explanation

First find the cube of 842³, which is 596,516,648

Next, find the cube of 800³, which is 512,000,000

Now, find the difference between them using the subtraction method. 596,516,648 – 512,000,000 = 84,516,648

Therefore, 842³ is 84,516,648 larger than 800³.

Well explained 👍

Problem 4

If a cube with a side length of 842 cm is compared to a cube with a side length of 42 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 842 cm is 596,516,648 cm³.

Explanation

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

Cubing 842 means multiplying 842 by itself three times: 842 × 842 = 708,724, and then 708,724 × 842 = 596,516,648.

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

Therefore, the volume of the cube is 596,516,648 cm³.

Well explained 👍

Problem 5

Estimate the cube of 841.9 using the cube of 842.

Okay, lets begin

The cube of 841.9 is approximately 596,516,648.

Explanation

First, identify the cube of 842.

The cube of 842 is 842³ = 596,516,648.

Since 841.9 is only a tiny bit less than 842, the cube of 841.9 will be almost the same as the cube of 842.

The cube of 841.9 is approximately 596,516,648 because the difference between 841.9 and 842 is very small.

So, we can approximate the value as 596,516,648.

Well explained 👍

FAQs on Cube of 842

1.What are the perfect cubes up to 842?

The perfect cubes up to 842 are 1, 8, 27, 64, 125, 216, and 343.

2.How do you calculate 842³?

To calculate 842³, use the multiplication method, 842 × 842 × 842, which equals 596,516,648.

3.What is the meaning of 842³?

842³ means 842 multiplied by itself three times, or 842 × 842 × 842.

4.What is the cube root of 842?

5.Is 842 a perfect cube?

No, 842 is not a perfect cube because no integer multiplied by itself three times equals 842.

Important Glossary for Cube of 842

  • 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: 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 amount of space occupied by a cube, calculated as the cube of its side length, V = Side³.
  • 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.