100 LearnersLast updated on June 1st, 2025
Cube of 384
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 384.
Cube of 384
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 384 can be written as 384³, which is the exponential form.
Or it can also be written in arithmetic form as, 384 × 384 × 384.
How to Calculate the Value of Cube of 384
In order to check whether a number is a cube number or not, we can use the following three methods: multiplication method, 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 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. 384³ = 384 × 384 × 384
Step 2: You get 56,623,104 as the answer. Hence, the cube of 384 is 56,623,104.
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 384 into two parts, as 300 and 84. Let a = 300 and b = 84, so a + b = 384
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 300³ 3a²b = 3 × 300² × 84 3ab² = 3 × 300 × 84² b³ = 84³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (300 + 84)³ = 300³ + 3 × 300² × 84 + 3 × 300 × 84² + 84³ 384³ = 27,000,000 + 22,680,000 + 6,364,800 + 592,704 384³ = 56,637,504
Step 5: Hence, the cube of 384 is 56,637,504.
Using a Calculator
To find the cube of 384 using a calculator, input the number 384 and use the cube function (if available) or multiply 384 × 384 × 384. This operation calculates the value of 384³, resulting in 56,623,104. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 3 followed by 8 and 4
Step 3: If the calculator has a cube function, press it to calculate 384³.
Step 4: If there is no cube function on the calculator, simply multiply 384 three times manually.
Step 5: The calculator will display 56,623,104.
Tips and Tricks for the Cube of 384
- 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 384
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, 384 × 384 and not 384 × 384 × 384. Always remember that 384³ = 384 × 384 × 384.
Solved Examples on Cube of 384
Problem 1
What is the cube and cube root of 384?
The cube of 384 is 56,623,104, and the cube root of 384 is approximately 7.273.
Explanation
First, let’s find the cube of 384.
We know that the cube of a number is expressed as x³ = y, where x is the given number, and y is the cubed value of that number.
So, we get 384³ = 56,623,104.
Next, we must find the cube root of 384.
We know that the cube root of a number ‘x’ is expressed as ∛x = y, where ‘x’ is the given number, and y is the cube root value of the number.
So, we get ∛384 ≈ 7.273.
Hence, the cube of 384 is 56,623,104, and the cube root of 384 is approximately 7.273.
Problem 2
If the side length of the cube is 384 cm, what is the volume?
The volume is 56,623,104 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 384 for the side length: V = 384³ = 56,623,104 cm³.
Problem 3
How much larger is 384³ than 300³?
384³ – 300³ = 29,623,104.
Explanation
First, find the cube of 384³, that is 56,623,104.
Next, find the cube of 300³, which is 27,000,000.
Now, find the difference between them using the subtraction method. 56,623,104 – 27,000,000 = 29,623,104.
Therefore, 384³ is 29,623,104 larger than 300³.
Problem 4
If a cube with a side length of 384 cm is compared to a cube with a side length of 84 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 384 cm is 56,623,104 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 384 means multiplying 384 by itself three times: 384 × 384 = 147,456, and then 147,456 × 384 = 56,623,104.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 56,623,104 cm³.
Problem 5
Estimate the cube 383.9 using the cube 384.
The cube of 383.9 is approximately 56,623,104.
Explanation
First, identify the cube of 384.
The cube of 384 is 384³ = 56,623,104.
Since 383.9 is only a tiny bit less than 384, the cube of 383.9 will be almost the same as the cube of 384.
The cube of 383.9 is approximately 56,623,104 because the difference between 383.9 and 384 is very small.
So, we can approximate the value as 56,623,104.
FAQs on Cube of 384
1.What are the perfect cubes up to 384?
2.How do you calculate 384³?
3.What is the meaning of 384³?
4.What is the cube root of 384?
5.Is 384 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 384?
8.How do technology and digital tools in United States support learning Algebra and Cube of 384?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of 384
- 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 to 8.
- Perfect Cube: A number that can be expressed as the product of three equal integers. For example, 27 is a perfect cube because it can be written as 3 × 3 × 3.
- Volume of a Cube: The amount of space inside a cube, calculated as the cube of its side length.
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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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