101 LearnersLast updated on June 3rd, 2025
Cube of 128
When a number is multiplied by itself three times, the resultant number is called the cube of the number. Cubing is used when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 128.
Cube of 128
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 128 can be written as 128³, which is the exponential form.
Or it can also be written in arithmetic form as, 128 × 128 × 128.
How to Calculate the Value of Cube of 128
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 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 numbers or quantities by combining them through repeated multiplication. It is a fundamental operation that forms the basis for more complex mathematical concepts.
Step 1: Write down the cube of the given number. 128³ = 128 × 128 × 128
Step 2: You get 2,097,152 as the answer. Hence, the cube of 128 is 2,097,152.
Using a Formula (a³)
The binomial formula (a + b)³ is used for finding the cube of a number. The formula is expanded as a³ + 3a²b + 3ab² + b³.
Step 1: Split the number 128 into two parts. Let a = 120 and b = 8, so a + b = 128.
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³.
Step 3: Calculate each term. a³ = 120³ 3a²b = 3 × 120² × 8 3ab² = 3 × 120 × 8² b³ = 8³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (120 + 8)³ = 120³ + 3 × 120² × 8 + 3 × 120 × 8² + 8³ 128³ = 1,728,000 + 345,600 + 23,040 + 512 128³ = 2,097,152
Step 5: Hence, the cube of 128 is 2,097,152.
Using a Calculator
To find the cube of 128 using a calculator, input the number 128 and use the cube function (if available) or multiply 128 × 128 × 128. This operation calculates the value of 128³, resulting in 2,097,152. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 1 followed by 2 and 8.
Step 3: If the calculator has a cube function, press it to calculate 128³.
Step 4: If there is no cube function on the calculator, simply multiply 128 three times manually.
Step 5: The calculator will display 2,097,152.
Tips and Tricks for the Cube of 128
- 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 128
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, 128 × 128 and not 128 × 128 × 128. Always remember that 128³ = 128 × 128 × 128.
Solved Examples on Cube of 128
Problem 1
What is the cube and cube root of 128?
The cube of 128 is 2,097,152 and the cube root of 128 is approximately 5.039.
Explanation
First, let’s find the cube of 128.
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 128³ = 2,097,152.
Next, we must find the cube root of 128.
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 ∛128 ≈ 5.039.
Hence, the cube of 128 is 2,097,152 and the cube root of 128 is approximately 5.039.
Problem 2
If the side length of the cube is 128 cm, what is the volume?
The volume is 2,097,152 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 128 for the side length: V = 128³ = 2,097,152 cm³.
Problem 3
How much larger is 128³ than 100³?
128³ – 100³ = 1,697,152.
Explanation
First, find the cube of 128, which is 2,097,152.
Next, find the cube of 100, which is 1,000,000.
Now, find the difference between them using the subtraction method. 2,097,152 – 1,000,000 = 1,097,152.
Therefore, 128³ is 1,097,152 larger than 100³.
Problem 4
If a cube with a side length of 128 cm is compared to a cube with a side length of 64 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 128 cm is 1,728,000 cm³ larger than the volume of the cube with a side length of 64 cm.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 128 means multiplying 128 by itself three times: 128 × 128 × 128 = 2,097,152.
Similarly, the volume of the cube with a side length of 64 cm is 64 × 64 × 64 = 262,144.
The difference in volume is 2,097,152 - 262,144 = 1,834,368.
Therefore, the volume of the cube with a side length of 128 cm is 1,834,368 cm³ larger than the volume of the cube with a side length of 64 cm.
Problem 5
Estimate the cube of 127.9 using the cube of 128.
The cube of 127.9 is approximately 2,097,152.
Explanation
First, identify the cube of 128,
The cube of 128 is 128³ = 2,097,152.
Since 127.9 is only a tiny bit less than 128, the cube of 127.9 will be almost the same as the cube of 128.
Therefore, the cube of 127.9 is approximately 2,097,152 because the difference between 127.9 and 128 is very small.
Hence, we approximate the value as 2,097,152.
FAQs on Cube of 128
1.What are the perfect cubes up to 128?
2.How do you calculate 128³?
3.What is the meaning of 128³?
4.What is the cube root of 128?
5.Is 128 a perfect cube?
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Cube of 128?
8.How do technology and digital tools in Philippines support learning Algebra and Cube of 128?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for Cube of 128
- 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 identical integers.
- Cube Root: The number which produces a given number when cubed. For example, the cube root of 8 is 2 because 2³ = 8.
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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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