113 LearnersLast updated on May 30th, 2025
Cube of 406
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 the cube of 406.
Cube of 406
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 406 can be written as 406³, which is the exponential form.
Or it can also be written in arithmetic form as, 406 × 406 × 406.
How to Calculate the Value of Cube of 406
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. 406³ = 406 × 406 × 406
Step 2: You get 66,847,016 as the answer. Hence, the cube of 406 is 66,847,016.
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 406 into two parts. Let a = 400 and b = 6, so a + b = 406
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × 6 3ab² = 3 × 400 × 6² b³ = 6³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 + 6)³ = 400³ + 3 × 400² × 6 + 3 × 400 × 6² + 6³ 406³ = 64,000,000 + 2,880,000 + 43,200 + 216 406³ = 66,847,416
Step 5: Hence, the cube of 406 is 66,847,416.
Using a Calculator
To find the cube of 406 using a calculator, input the number 406 and use the cube function (if available) or multiply 406 × 406 × 406. This operation calculates the value of 406³, resulting in 66,847,016. 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 0 and then 6.
Step 3: If the calculator has a cube function, press it to calculate 406³.
Step 4: If there is no cube function on the calculator, simply multiply 406 three times manually.
Step 5: The calculator will display 66,847,016.
Tips and Tricks for the Cube of 406
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 406
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:
Mistake 1
Incorrect Multiplication
Kids might multiply the numbers only twice. That is, 406 × 406 and not 406 × 406 × 406. Always remember that 406³ = 406 × 406 × 406.
Solved Examples on Cube of 406
Problem 1
What is the cube and cube root of 406?
The cube of 406 is 66,847,016 and the cube root of 406 is approximately 7.403.
Explanation
First, let’s find the cube of 406.
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 406³ = 66,847,016. Next, we must find the cube root of 406.
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 ∛406 ≈ 7.403.
Hence the cube of 406 is 66,847,016 and the cube root of 406 is approximately 7.403.
Problem 2
If the side length of a cube is 406 cm, what is the volume?
The volume is 66,847,016 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 406 for the side length: V = 406³ = 66,847,016 cm³.
Problem 3
How much larger is 406³ than 400³?
406³ – 400³ = 2,847,016.
Explanation
First, find the cube of 406³, that is 66,847,016.
Next, find the cube of 400³, which is 64,000,000.
Now, find the difference between them using the subtraction method. 66,847,016 – 64,000,000 = 2,847,016.
Therefore, 406³ is 2,847,016 larger than 400³.
Problem 4
If a cube with a side length of 406 cm is compared to a cube with a side length of 20 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 406 cm is 66,847,016 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 406 means multiplying 406 by itself three times: 406 × 406 = 164,836, and then 164,836 × 406 = 66,847,016.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 66,847,016 cm³.
Problem 5
Estimate the cube of 405.9 using the cube of 406.
The cube of 405.9 is approximately 66,847,016.
Explanation
First, identify the cube of 406.
The cube of 406 is 406³ = 66,847,016.
Since 405.9 is only a tiny bit less than 406, the cube of 405.9 will be almost the same as the cube of 406.
The cube of 405.9 is approximately 66,847,016 because the difference between 405.9 and 406 is very small.
So, we can approximate the value as 66,847,016.
FAQs on Cube of 406
1.What are the perfect cubes up to 406?
2.How do you calculate 406³?
3.What is the meaning of 406³?
4.What is the cube root of 406?
5.Is 406 a perfect cube?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Cube of 406?
8.How do technology and digital tools in United States support learning Algebra and Cube of 406?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of 406
- 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 of a Cube: The amount of space inside a cube, calculated by raising the length of its side to the power of three.
- Perfect Cube: A number that can be expressed as the cube of an integer.
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Jaskaran Singh Saluja
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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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