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104 LearnersLast updated on September 18, 2025
Cube of 1428
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 1428.
Cube of 1428
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 1428 can be written as 1428³, which is the exponential form. Or it can also be written in arithmetic form as 1428 × 1428 × 1428.
How to Calculate the Value of Cube of 1428
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 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 a number by combining it 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. 1428³ = 1428 × 1428 × 1428
Step 2: Calculate the product: Hence, the cube of 1428 is 2,913,897,152.
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 1428 into two parts, as 1400 and 28. Let a = 1400 and b = 28, so a + b = 1428
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 1400³
3a²b = 3 × 1400² × 28
3ab² = 3 × 1400 × 28²
b³ = 28³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³
(1400 + 28)³ = 1400³ + 3 × 1400² × 28 + 3 × 1400 × 28² + 28³
1428³ = 2,744,000,000 + 164,640,000 + 1,649,280 + 21,952
1428³ = 2,913,897,152
Step 5: Hence, the cube of 1428 is 2,913,897,152.
Using a Calculator
To find the cube of 1428 using a calculator, input the number 1428 and use the cube function (if available) or multiply 1428 × 1428 × 1428. This operation calculates the value of 1428³, resulting in 2,913,897,152. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Enter 1428.
Step 3: If the calculator has a cube function, press it to calculate 1428³.
Step 4: If there is no cube function on the calculator, simply multiply 1428 three times manually.
Step 5: The calculator will display 2,913,897,152.
Tips and Tricks for the Cube of 1428
- 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 1428
There are some typical errors that one might make 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
One might multiply the numbers only twice. That is, 1428 × 1428 and not 1428 × 1428 × 1428. Always remember that 1428³ = 1428 × 1428 × 1428.
Mistake 2
Misunderstanding the Cube Formula
There is a possibility of confusion between the formulas of square numbers and cube numbers. The square number formula is (a + b)² and the cube number formula is (a + b)³. Always review the formula for the difference between squaring and cubing.
Mistake 3
Calculator Misuse
One might press the wrong buttons, such as using the square (x²) function instead of the cube (x³) function or skipping steps in manual multiplication. Always double-check your inputs on the calculator, and if it lacks a cube function, perform the multiplication in steps.
Mistake 4
Misplacing Zeros
Misplacing zeros during manual multiplication leads to incorrect results like 291,389,715 instead of 2,913,897,152. Always double-check your answers.
Mistake 5
Ignoring the Binomial Formula
One might attempt to split the 1428 into 1400 + 28, but not apply the correct binomial expansion. To avoid this, carefully calculate each term step-by-step during the application of the formula.
Solved Examples on Cube of 1428
Problem 1
What is the cube and cube root of 1428?
The cube of 1428 is 2,913,897,152 and the cube root of 1428 is approximately 11.152.
Explanation
First, let’s find the cube of 1428.
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 1428³ = 2,913,897,152.
Next, we must find the cube root of 1428. 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 ∛1428 ≈ 11.152 Hence the cube of 1428 is 2,913,897,152 and the cube root of 1428 is approximately 11.152.
Problem 2
If the side length of the cube is 1428 cm, what is the volume?
The volume is 2,913,897,152 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 1428 for the side length: V = 1428³ = 2,913,897,152 cm³.
Problem 3
How much larger is 1428³ than 1000³?
1428³ – 1000³ = 2,913,897,152 – 1,000,000,000 = 1,913,897,152.
Explanation
First find the cube of 1428, that is 2,913,897,152.
Next, find the cube of 1000, which is 1,000,000,000.
Now, find the difference between them using the subtraction method. 2,913,897,152 – 1,000,000,000 = 1,913,897,152
Therefore, 1428³ is 1,913,897,152 larger than 1000³.
Problem 4
If a cube with a side length of 1428 cm is compared to a cube with a side length of 200 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 1428 cm is 2,913,897,152 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 1428 means multiplying 1428 by itself three times: 1428 × 1428 × 1428 = 2,913,897,152.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 2,913,897,152 cm³.
Problem 5
Estimate the cube of 1427 using the cube of 1428.
The cube of 1427 is approximately 2,913,897,152.
Explanation
First, identify the cube of 1428, The cube of 1428 is 1428³ = 2,913,897,152.
Since 1427 is only a tiny bit less than 1428, the cube of 1427 will be almost the same as the cube of 1428.
The cube of 1427 is approximately 2,913,897,152 because the difference between 1427 and 1428 is very small.
So, we can approximate the value as 2,913,897,152.
FAQs on Cube of 1428
1.What are the perfect cubes up to 1428?
2.How do you calculate 1428³?
3.What is the meaning of 1428³?
4.What is the cube root of 1428?
5.Is 1428 a perfect cube?
Important Glossaries for Cube of 1428
- Binomial Formula: 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: 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, which equals 8.
- Perfect Cube: A number that can be expressed as the cube of an integer.
- Cube Root: The value that, when multiplied by itself three times, gives the original number.
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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.
