Cube of 420
2026-02-28 17:58 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 420.

Cube of 420

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 420 can be written as 4203, which is the exponential form.

Or it can also be written in arithmetic form as, 420 × 420 × 420.

How to Calculate the Value of Cube of 420

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.

  • 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. 4203 = 420 × 420 × 420

Step 2: You get 74,088,000 as the answer. Hence, the cube of 420 is 74,088,000.

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Using a Formula a^3

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 420 into two parts, as and . Let a = 400 and b = 20, so a + b = 420

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

Step 3: Calculate each term a3 = 4003 3a2b = 3 × 4002 × 20 3ab2 = 3 × 400 × 202 b3 = 203

Step 4: Add all the terms together: (a + b)3 = a3 + 3a2b + 3ab2 + b3 (400 + 20)3 = 4003 + 3 × 4002 × 20 + 3 × 400 × 202 + 203 4203 = 64,000,000 + 9,600,000 + 960,000 + 8,000 4203 = 74,088,000

Step 5: Hence, the cube of 420 is 74,088,000.

Using a Calculator

To find the cube of 420 using a calculator, input the number 420 and use the cube function (if available) or multiply 420 × 420 × 420. This operation calculates the value of 4203, resulting in 74,088,000. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 4 followed by 2 and 0

Step 3: If the calculator has a cube function, press it to calculate 4203.

Step 4: If there is no cube function on the calculator, simply multiply 420 three times manually.

Step 5: The calculator will display 74,088,000.

Tips and Tricks for the Cube of 420

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 420

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 420?

Okay, lets begin

The cube of 420 is 74,088,000 and the cube root of 420 is approximately 7.476.

Explanation

First, let’s find the cube of 420.

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 4203 = 74,088,000

Next, we must find the cube root of 420

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 ∛420} ≈ 7.476

Hence the cube of 420 is 74,088,000 and the cube root of 420 is approximately 7.476.

Well explained 👍

Problem 2

If the side length of the cube is 420 cm, what is the volume?

Okay, lets begin

The volume is 74,088,000 cm³.

Explanation

Use the volume formula for a cube V = Side3.

Substitute 420 for the side length: V = 4203 = 74,088,000cm³.

Well explained 👍

Problem 3

How much larger is \(420^3\) than \(400^3\)?

Okay, lets begin

4203 - 4003 = 10,088,000.

Explanation

First, find the cube of 4203, that is 74,088,000

Next, find the cube of 4003, which is 64,000,000

Now, find the difference between them using the subtraction method. 74,088,000 - 64,000,000 = 10,088,000

Therefore, the 4203 is 10,088,000 larger than 4003.

Well explained 👍

Problem 4

If a cube with a side length of 420 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 420 cm is 74,088,000 cm³

Explanation

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

Cubing 420 means multiplying 420 by itself three times: 420 × 420 = 176,400, and then 176,400 × 420 = 74,088,000.

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

Therefore, the volume of the cube is 74,088,000 cm³.

Well explained 👍

Problem 5

Estimate the cube of 419.9 using the cube of 420.

Okay, lets begin

The cube of 419.9 is approximately 74,088,000.

Explanation

First, identify the cube of 420, The cube of 420 is 4203 = 74,088,000.

Since 419.9 is only a tiny bit less than 420, the cube of 419.9 will be almost the same as the cube of 420.

The cube of 419.9 is approximately 74,088,000 because the difference between 419.9 and 420 is very small.

So, we can approximate the value as 74,088,000.

Well explained 👍

FAQs on Cube of 420

1.What are the perfect cubes up to 420?

The perfect cubes up to 420 are 1, 8, 27, 64, 125, 216, and 343.

2.How do you calculate \(420^3\)?

To calculate 4203, use the multiplication method, 420 × 420 × 420, which equals 74,088,000.

3.What is the meaning of \(420^3\)?

4203 means 420 multiplied by itself three times, or 420 × 420 × 420.

4.What is the cube root of 420?

5.Is 420 a perfect cube?

No, 420 is not a perfect cube because no integer multiplied by itself three times equals 420.

Important Glossaries for Cube of 420

  • 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 to 8.
  • Volume of a Cube: The volume of a cube is calculated by raising the side length to the power of three, V = Side3.
  • Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number. It is represented as ∛x.

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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.