114 LearnersLast updated on May 30th, 2025
Cube of 238
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 238.
Cube of 238
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 238 can be written as 238³, which is the exponential form.
Or it can also be written in arithmetic form as, 238 × 238 × 238.
How to Calculate the Value of Cube of 238
In order to check whether a number is a cube number or not, we can use the following three methods, such as the multiplication method, a 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 (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. 238³ = 238 × 238 × 238
Step 2: You get 13,472,872 as the answer.
Hence, the cube of 238 is 13,472,872.
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 238 into two parts, as 230 and 8. Let a = 230 and b = 8, so a + b = 238
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 230³ 3a²b = 3 × 230² × 8 3ab² = 3 × 230 × 8² b³ = 8³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (230 + 8)³ = 230³ + 3 × 230² × 8 + 3 × 230 × 8² + 8³ 238³ = 12,167,000 + 127,920 + 44,160 + 512 238³ = 13,472,872
Step 5: Hence, the cube of 238 is 13,472,872.
Using a Calculator
To find the cube of 238 using a calculator, input the number 238 and use the cube function (if available) or multiply 238 × 238 × 238. This operation calculates the value of 238³, resulting in 13,472,872. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 2 followed by 3 and then 8
Step 3: If the calculator has a cube function, press it to calculate 238³.
Step 4: If there is no cube function on the calculator, simply multiply 238 three times manually.
Step 5: The calculator will display 13,472,872.
Tips and Tricks for the Cube of 238
- 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 238
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, 238 × 238 and not 238 × 238 × 238. Always remember that 238³ = 238 × 238 × 238.
Solved Examples on Cube of 238
Problem 1
What is the cube and cube root of 238?
The cube of 238 is 13,472,872 and the cube root of 238 is approximately 6.2.
Explanation
First, let’s find the cube of 238.
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 238³ = 13,472,872 Next, we must find the cube root of 238
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√238 ≈ 6.2
Hence the cube of 238 is 13,472,872 and the cube root of 238 is approximately 6.2.
Problem 2
If the side length of the cube is 238 cm, what is the volume?
The volume is 13,472,872 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 238 for the side length: V = 238³ = 13,472,872 cm³.
Problem 3
How much larger is 238³ than 230³?
238³ – 230³ = 1,305,872.
Explanation
First, find the cube of 238³, which is 13,472,872
Next, find the cube of 230³, which is 12,167,000
Now, find the difference between them using the subtraction method. 13,472,872 – 12,167,000 = 1,305,872
Therefore, 238³ is 1,305,872 larger than 230³.
Problem 4
If a cube with a side length of 238 cm is compared to a cube with a side length of 10 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 238 cm is 13,472,872 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 238 means multiplying 238 by itself three times: 238 × 238 = 56,644, and then 56,644 × 238 = 13,472,872.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 13,472,872 cm³.
Problem 5
Estimate the cube of 237.9 using the cube of 238.
The cube of 237.9 is approximately 13,472,872.
Explanation
First, identify the cube of 238,
The cube of 238 is 238³ = 13,472,872.
Since 237.9 is only a tiny bit less than 238, the cube of 237.9 will be almost the same as the cube of 238.
The cube of 237.9 is approximately 13,472,872 because the difference between 237.9 and 238 is very small.
So, we can approximate the value as 13,472,872.
FAQs on Cube of 238
1.What are the perfect cubes up to 238?
2.How do you calculate 238³?
3.What is the meaning of 238³?
4.What is the cube root of 238?
5.Is 238 a perfect cube?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Cube of 238?
8.How do technology and digital tools in Oman support learning Algebra and Cube of 238?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for Cube of 238
- 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: The number that, when multiplied by itself twice, 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.
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