116 LearnersLast updated on May 28th, 2025
Cube of 472
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is useful when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 472.
Cube of 472
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 472 can be written as 472³, which is the exponential form. Or it can also be written in arithmetic form as 472 × 472 × 472.
How to Calculate the Value of Cube of 472
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 students 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. 472³ = 472 × 472 × 472
Step 2: You get 105,884,928 as the answer. Hence, the cube of 472 is 105,884,928.
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 472 into two parts. Let a = 470 and b = 2, so a + b = 472
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 470³ 3a²b = 3 × 470² × 2 3ab² = 3 × 470 × 2² b³ = 2³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(470 + 2)³ = 470³ + 3 × 470² × 2 + 3 × 470 × 2² + 2³
472³ = 103823000 + 1323000 + 5640 + 8
472³ = 105,884,928
Step 5: Hence, the cube of 472 is 105,884,928.
Using a Calculator
To find the cube of 472 using a calculator, input the number 472 and use the cube function (if available) or multiply 472 × 472 × 472. This operation calculates the value of 472³, resulting in 105,884,928. 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 7 and 2
Step 3: If the calculator has a cube function, press it to calculate 472³.
Step 4: If there is no cube function on the calculator, simply multiply 472 three times manually.
Step 5: The calculator will display 105,884,928.
Tips and Tricks for the Cube of 472
- 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 472
There are some typical errors that students might make during the process of cubing a number. Let us take a look at five of the major mistakes that students might make:
Mistake 1
Incorrect Multiplication
Students might multiply the numbers only twice. That is, 472 × 472 and not 472 × 472 × 472. Always remember that 472³ = 472 × 472 × 472.
Solved Examples on Cube of 472
Problem 1
What is the cube and cube root of 472?
The cube of 472 is 105,884,928 and the cube root of 472 is approximately 7.778.
Explanation
First, let’s find the cube of 472.
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 472³ = 105,884,928
Next, we must find the cube root of 472 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 ∛472 ≈ 7.778
Hence, the cube of 472 is 105,884,928 and the cube root of 472 is approximately 7.778.
Problem 2
If the side length of a cube is 472 cm, what is the volume?
The volume is 105,884,928 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 472 for the side length: V = 472³ = 105,884,928 cm³.
Problem 3
How much larger is 472³ than 470³?
472³ – 470³ = 2,061,928.
Explanation
First find the cube of 472³, which is 105,884,928
Next, find the cube of 470³, which is 103,823,000
Now, find the difference between them using the subtraction method.
105,884,928 – 103,823,000 = 2,061,928
Therefore, 472³ is 2,061,928 larger than 470³.
Problem 4
If a cube with a side length of 472 cm is compared to a cube with a side length of 2 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 472 cm is 105,884,928 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 472 means multiplying 472 by itself three times: 472 × 472 = 222,784, and then 222,784 × 472 = 105,884,928.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 105,884,928 cm³.
Problem 5
Estimate the cube of 471.9 using the cube of 472.
The cube of 471.9 is approximately 105,884,928.
Explanation
First, identify the cube of 472, The cube of 472 is 472³ = 105,884,928.
Since 471.9 is only a tiny bit less than 472, the cube of 471.9 will be almost the same as the cube of 472.
The cube of 471.9 is approximately 105,884,928 because the difference between 471.9 and 472 is very small.
So, we can approximate the value as 105,884,928.
FAQs on Cube of 472
1.What are the perfect cubes up to 472?
2.How do you calculate 472³?
3.What is the meaning of 472³?
4.What is the cube root of 472?
5.Is 472 a perfect cube?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Cube of 472?
8.How do technology and digital tools in Qatar support learning Algebra and Cube of 472?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for Cube of 472
- 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.
- Perfect Cube: A number that can be expressed as the product of three equal integers, such as 27, which is 3 × 3 × 3.
- Volume of a Cube: The amount of space enclosed within a cube, calculated as the side length raised to the third power, or side × side × side.
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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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