115 LearnersLast updated on May 30th, 2025
Cube of 231
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 cubes of 231.
Cube of 231
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 by itself three times results in a negative number.
The cube of 231 can be written as 231³, which is the exponential form.
Or it can also be written in arithmetic form as 231 × 231 × 231.
How to Calculate the Value of Cube of 231
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 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. 231³ = 231 × 231 × 231
Step 2: You get 12,345,631 as the answer.
Hence, the cube of 231 is 12,345,631.
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 231 into two parts. Let a = 230 and b = 1, so a + b = 231
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 230³ 3a²b = 3 × 230² × 1 3ab² = 3 × 230 × 1² b³ = 1³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (230 + 1)³ = 230³ + 3 × 230² × 1 + 3 × 230 × 1² + 1³ 231³ = 12,167,000 + 158,700 + 690 + 1 231³ = 12,345,631
Step 5: Hence, the cube of 231 is 12,345,631.
Using a Calculator
To find the cube of 231 using a calculator, input the number 231 and use the cube function (if available) or multiply 231 × 231 × 231. This operation calculates the value of 231³, resulting in 12,345,631. 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 1
Step 3: If the calculator has a cube function, press it to calculate 231³.
Step 4: If there is no cube function on the calculator, simply multiply 231 three times manually.
Step 5: The calculator will display 12,345,631.
Tips and Tricks for the Cube of 231
- 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 231
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, 231 × 231 and not 231 × 231 × 231. Always remember that 231³ = 231 × 231 × 231.
Solved Examples on Cube of 231
Problem 1
What is the cube and cube root of 231?
The cube of 231 is 12,345,631 and the cube root of 231 is approximately 6.165.
Explanation
First, let’s find the cube of 231.
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 231³ = 12,345,631 Next, we must find the cube root of 231.
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√231 ≈ 6.165
Hence the cube of 231 is 12,345,631 and the cube root of 231 is approximately 6.165.
Problem 2
If the side length of the cube is 231 cm, what is the volume?
The volume is 12,345,631 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 231 for the side length: V = 231³ = 12,345,631 cm³.
Problem 3
How much larger is 231³ than 101³?
231³ – 101³ = 12,334,471.
Explanation
First find the cube of 231, which is 12,345,631.
Next, find the cube of 101, which is 1,160,801.
Now, find the difference between them using the subtraction method. 12,345,631 – 1,160,801 = 12,334,471
Therefore, 231³ is 12,334,471 larger than 101³.
Problem 4
If a cube with a side length of 231 cm is compared to a cube with a side length of 11 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 231 cm is 12,345,631 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 231 means multiplying 231 by itself three times: 231 × 231 = 53,361, and then 53,361 × 231 = 12,345,631.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 12,345,631 cm³.
Problem 5
Estimate the cube of 230.9 using the cube of 231.
The cube of 230.9 is approximately 12,345,631.
Explanation
First, identify the cube of 231.
The cube of 231 is 231³ = 12,345,631.
Since 230.9 is only a tiny bit less than 231, the cube of 230.9 will be almost the same as the cube of 231.
The cube of 230.9 is approximately 12,345,631 because the difference between 230.9 and 231 is very small.
So, we can approximate the value as 12,345,631.
FAQs on Cube of 231
1.What are the perfect cubes up to 231?
2.How do you calculate 231³?
3.What is the meaning of 231³?
4.What is the cube root of 231?
5.Is 231 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 231?
8.How do technology and digital tools in Philippines support learning Algebra and Cube of 231?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for Cube of 231
- Binomial Formula: An algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer. The formula is used to find the 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 equals 8.
- Perfect Cube: A number that can be expressed as the cube of an integer.
- Multiplication Method: A mathematical process used to find the product of numbers by repeated addition, forming the basis for more complex mathematical concepts.
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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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