115 LearnersLast updated on May 28th, 2025
Cube of 477
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 477.
Cube of 477
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 477 can be written as 477³, which is the exponential form. Or it can also be written in arithmetic form as, 477 × 477 × 477.
How to Calculate the Value of the Cube of 477
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
- 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. 477³ = 477 × 477 × 477
Step 2: You get 108,919,833 as the answer. Hence, the cube of 477 is 108,919,833.
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 477 into two parts. Let a = 470 and b = 7, so a + b = 477
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 470³
3a²b = 3 × 470² × 7
3ab² = 3 × 470 × 7²
b³ = 7³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(470 + 7)³ = 470³ + 3 × 470² × 7 + 3 × 470 × 7² + 7³
Step 5: Hence, the cube of 477 is 108,919,833.
Using a Calculator
To find the cube of 477 using a calculator, input the number 477 and use the cube function (if available) or multiply 477 × 477 × 477. This operation calculates the value of 477³, resulting in 108,919,833. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Enter 477
Step 3: If the calculator has a cube function, press it to calculate 477³.
Step 4: If there is no cube function on the calculator, simply multiply 477 three times manually.
Step 5: The calculator will display 108,919,833.
Tips and Tricks for the Cube of 477
- 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 477
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, 477 × 477 and not 477 × 477 × 477. Always remember that 477³ = 477 × 477 × 477.
Solved Examples on Cube of 477
Problem 1
What is the cube and cube root of 477?
The cube of 477 is 108,919,833 and the cube root of 477 is approximately 7.800.
Explanation
First, let’s find the cube of 477.
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 477³ = 108,919,833.
Next, we must find the cube root of 477. 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 ∛477 ≈ 7.800.
Hence, the cube of 477 is 108,919,833 and the cube root of 477 is approximately 7.800.
Problem 2
If the side length of a cube is 477 cm, what is the volume?
The volume is 108,919,833 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 477 for the side length: V = 477³ = 108,919,833 cm³.
Problem 3
How much larger is 477³ than 470³?
477³ – 470³ = 15,505,833.
Explanation
First, find the cube of 477³, which is 108,919,833.
Next, find the cube of 470³, which is 93,414,000.
Now, find the difference between them using the subtraction method.
108,919,833 – 93,414,000 = 15,505,833.
Therefore, 477³ is 15,505,833 larger than 470³.
Problem 4
If a cube with a side length of 477 cm is compared to a cube with a side length of 7 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 477 cm is 108,919,833 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 477 means multiplying 477 by itself three times: 477 × 477 = 227,529, and 227,529 × 477 = 108,919,833.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 108,919,833 cm³.
Problem 5
Estimate the cube of 476.9 using the cube of 477.
The cube of 476.9 is approximately 108,919,833.
Explanation
First, identify the cube of 477, The cube of 477 is 477³ = 108,919,833.
Since 476.9 is only a tiny bit less than 477, the cube of 476.9 will be almost the same as the cube of 477.
The cube of 476.9 is approximately 108,919,833 because the difference between 476.9 and 477 is very small.
So, we can approximate the value as 108,919,833.
FAQs on Cube of 477
1.What are the perfect cubes up to 477?
2.How do you calculate 477³?
3.What is the meaning of 477³?
4.What is the cube root of 477?
5.Is 477 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 477?
8.How do technology and digital tools in United States support learning Algebra and Cube of 477?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of 477
- 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.
- Multiplication Method: A mathematical process used to find the product of numbers by combining them through repeated addition.
- Volume of a Cube: The amount of space occupied by a cube, calculated by raising the side length to the power of three.
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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
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