114 LearnersLast updated on May 30th, 2025
Cube of 223
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 223.
Cube of 223
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 223 can be written as 223³, which is the exponential form.
Or it can also be written in arithmetic form as, 223 × 223 × 223.
How to Calculate the Value of Cube of 223
In order to check whether a number is a cube number or not, we can use the following three methods, such as 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. 223³ = 223 × 223 × 223
Step 2: You get 11,080,167 as the answer.
Hence, the cube of 223 is 11,080,167.
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 223 into two parts. Let a = 200 and b = 23, so a + b = 223
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 200³ 3a²b = 3 × 200² × 23 3ab² = 3 × 200 × 23² b³ = 23³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (200 + 23)³ = 200³ + 3 × 200² × 23 + 3 × 200 × 23² + 23³ 223³ = 8,000,000 + 2,760,000 + 317,400 + 12,167 223³ = 11,080,167
Step 5: Hence, the cube of 223 is 11,080,167.
Using a Calculator
To find the cube of 223 using a calculator, input the number 223 and use the cube function (if available) or multiply 223 × 223 × 223. This operation calculates the value of 223³, resulting in 11,080,167. 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 2 and 3
Step 3: If the calculator has a cube function, press it to calculate 223³.
Step 4: If there is no cube function on the calculator, simply multiply 223 three times manually.
Step 5: The calculator will display 11,080,167.
Tips and Tricks for the Cube of 223
- 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 223
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, 223 × 223 and not 223 × 223 × 223. Always remember that 223³ = 223 × 223 × 223.
Solved Examples on Cube of 223
Problem 1
What is the cube and cube root of 223?
The cube of 223 is 11,080,167 and the cube root of 223 is approximately 6.017.
Explanation
First, let’s find the cube of 223.
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 223³ = 11,080,167 Next, we must find the cube root of 223
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 ∛223 ≈ 6.017
Hence the cube of 223 is 11,080,167 and the cube root of 223 is approximately 6.017.
Problem 2
If the side length of the cube is 223 cm, what is the volume?
The volume is 11,080,167 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 223 for the side length: V = 223³ = 11,080,167 cm³.
Problem 3
How much larger is 223³ than 200³?
223³ – 200³ = 3,080,167.
Explanation
First find the cube of 223³, that is 11,080,167
Next, find the cube of 200³, which is 8,000,000
Now, find the difference between them using the subtraction method. 11,080,167 – 8,000,000 = 3,080,167
Therefore, the 223³ is 3,080,167 larger than 200³.
Problem 4
If a cube with a side length of 223 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 223 cm is 11,080,167 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 223 means multiplying 223 by itself three times: 223 × 223 = 49,729, and then 49,729 × 223 = 11,080,167.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 11,080,167 cm³.
Problem 5
Estimate the cube 222 using the cube 223.
The cube of 222 is approximately 11,080,167.
Explanation
First, identify the cube of 223,
The cube of 223 is 223³ = 11,080,167.
Since 222 is only a tiny bit less than 223, the cube of 222 will be almost the same as the cube of 223.
The cube of 222 is approximately 11,080,167 because the difference between 222 and 223 is very small.
So, we can approximate the value as 11,080,167.
FAQs on Cube of 223
1.What are the perfect cubes up to 223?
2.How do you calculate 223³?
3.What is the meaning of 223³?
4.What is the cube root of 223?
5.Is 223 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 223?
8.How do technology and digital tools in Oman support learning Algebra and Cube of 223?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for Cube of 223
- 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.
- Cube Root: The value that, when cubed, gives the original number. For example, the cube root of 8 is 2 because 2³ = 8.
- Volume of a Cube: The amount of space inside a cube, calculated as the side length cubed (Side³).
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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.
