100 LearnersLast updated on June 2nd, 2025
Cube of 428
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 428.
Cube of 428
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 428 can be written as 428³, which is the exponential form.
Or it can also be written in arithmetic form as 428 × 428 × 428.
How to Calculate the Value of Cube of 428
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 will help to cube 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. 428³ = 428 × 428 × 428
Step 2: You get 78,402,752 as the answer. Hence, the cube of 428 is 78,402,752.
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 428 into two parts. Let a = 400 and b = 28, so a + b = 428
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × 28 3ab² = 3 × 400 × 28² b³ = 28³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 + 28)³ = 400³ + 3 × 400² × 28 + 3 × 400 × 28² + 28³ 428³ = 64,000,000 + 13,440,000 + 1,344,000 + 21,952 428³ = 78,402,752
Step 5: Hence, the cube of 428 is 78,402,752.
Using a Calculator
To find the cube of 428 using a calculator, input the number 428 and use the cube function (if available) or multiply 428 × 428 × 428. This operation calculates the value of 428³, resulting in 78,402,752. 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 8
Step 3: If the calculator has a cube function, press it to calculate 428³.
Step 4: If there is no cube function on the calculator, simply multiply 428 three times manually.
Step 5: The calculator will display 78,402,752.
Tips and Tricks for the Cube of 428
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 428
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 that might occur:
Mistake 1
Incorrect Multiplication
Multiplying the numbers only twice. That is, 428 × 428 and not 428 × 428 × 428. Always remember that 428³ = 428 × 428 × 428.
Solved Examples on Cube of 428
Problem 1
What is the cube and cube root of 428?
The cube of 428 is 78,402,752 and the cube root of 428 is approximately 7.53.
Explanation
First, let’s find the cube of 428.
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 428³ = 78,402,752 Next, we must find the cube root of 428
We know that the cube root of a number ‘x’, such that ³√x = y
Where ‘x’ is the given number, and y is the cube root value of the number
So, we get ³√428 ≈ 7.53
Hence the cube of 428 is 78,402,752 and the cube root of 428 is approximately 7.53.
Problem 2
If the side length of the cube is 428 cm, what is the volume?
The volume is 78,402,752 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 428 for the side length: V = 428³ = 78,402,752 cm³.
Problem 3
How much larger is 428³ than 400³?
428³ – 400³ = 14,402,752.
Explanation
First find the cube of 428, which is 78,402,752
Next, find the cube of 400, which is 64,000,000
Now, find the difference between them using the subtraction method. 78,402,752 – 64,000,000 = 14,402,752
Therefore, 428³ is 14,402,752 larger than 400³.
Problem 4
If a cube with a side length of 428 cm is compared to a cube with a side length of 28 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 428 cm is 78,402,752 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a three-dimensional object).
Cubing 428 means multiplying 428 by itself three times: 428 × 428 = 183,184, and 183,184 × 428 = 78,402,752.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 78,402,752 cm³.
Problem 5
Estimate the cube 427.9 using the cube 428.
The cube of 427.9 is approximately 78,402,752.
Explanation
First, identify the cube of 428, The cube of 428 is 428³ = 78,402,752.
Since 427.9 is only a tiny bit less than 428, the cube of 427.9 will be almost the same as the cube of 428.
The cube of 427.9 is approximately 78,402,752 because the difference between 427.9 and 428 is very small.
So, we can approximate the value as 78,402,752.
FAQs on Cube of 428
1.What are the perfect cubes up to 428?
2.How do you calculate 428³?
3.What is the meaning of 428³?
4.What is the cube root of 428?
5.Is 428 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 428?
8.How do technology and digital tools in United States support learning Algebra and Cube of 428?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of 428
- 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 cube of an integer.
- Cube Root: A number that, when multiplied by itself three times, gives the original number. For example, the cube root of 8 is 2.
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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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