123 LearnersLast updated on June 3rd, 2025
Cube of 123
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 123.
Cube of 123
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 123 can be written as 123³, which is the exponential form.
Or it can also be written in arithmetic form as, 123 × 123 × 123.
How to Calculate the Value of Cube of 123
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
- 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. 123³ = 123 × 123 × 123
Step 2: You get 1,860,867 as the answer. Hence, the cube of 123 is 1,860,867.
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 123 into two parts. Let a = 120 and b = 3, so a + b = 123
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 120³ 3a²b = 3 × 120² × 3 3ab² = 3 × 120 × 3² b³ = 3³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (120 + 3)³ = 120³ + 3 × 120² × 3 + 3 × 120 × 3² + 3³ 123³ = 1,728,000 + 129,600 + 3,240 + 27 123³ = 1,860,867
Step 5: Hence, the cube of 123 is 1,860,867.
Using a Calculator
To find the cube of 123 using a calculator, input the number 123 and use the cube function (if available) or multiply 123 × 123 × 123. This operation calculates the value of 123³, resulting in 1,860,867. 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 then 3
Step 3: If the calculator has a cube function, press it to calculate 123³.
Step 4: If there is no cube function on the calculator, simply multiply 123 three times manually.
Step 5: The calculator will display 1,860,867.
Tips and Tricks for the Cube of 123
- 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 123
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, 123 × 123 and not 123 × 123 × 123. Always remember that 123³ = 123 × 123 × 123.
Mistake 2
Misunderstanding the Cube Formula
There is a possibility that kids might be confused between the formulas of square numbers and cube numbers. The square number formula is (a + b)² and the cube number formula is (a + b)³. Always review the formula for the difference between squaring and cubing.
Mistake 3
Calculator Misuse
Kids might press the wrong buttons, such as using the square (x²) function instead of the cube (x³) function or skipping steps in manual multiplication. Always double-check your inputs on the calculator, and if it lacks a cube function, perform the multiplication in steps.
Mistake 4
Misplacing Zeros
Misplacing zeros during manual multiplication leads to incorrect results like 186,086 instead of 1,860,867. For this, kids should always double-check their answers.
Mistake 5
Ignoring the Binomial Formula
Kids might attempt to split the 123 into 120 + 3, but not apply the correct binomial expansion. In order to avoid this, carefully calculate each term step-by-step during the application of the formula.
Solved Examples on Cube of 123
Problem 1
What is the cube and cube root of 123?
The cube of 123 is 1,860,867 and the cube root of 123 is approximately 4.986.
Explanation
First, let’s find the cube of 123.
We know that the cube of a number is calculated as x³ = y, where x is the given number, and y is the cubed value of that number. So, we get 123³ = 1,860,867.
Next, we must find the cube root of 123.
We know that the cube root of a number ‘x’ is such that ∛x = y, where ‘x’ is the given number, and y is the cube root value of the number.
So, we get ∛123 ≈ 4.986.
Hence the cube of 123 is 1,860,867 and the cube root of 123 is approximately 4.986.
Problem 2
If a cube has a side length of 123 cm, what is the volume?
The volume is 1,860,867 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 123 for the side length: V = 123³ = 1,860,867 cm³.
Problem 3
How much larger is 123³ than 120³?
123³ – 120³ = 132,867.
Explanation
First, find the cube of 123, which is 1,860,867.
Next, find the cube of 120, which is 1,728,000.
Now, find the difference between them using the subtraction method. 1,860,867 – 1,728,000 = 132,867.
Therefore, 123³ is 132,867 larger than 120³.
Problem 4
If a cube with a side length of 123 cm is compared to a cube with a side length of 3 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 123 cm is 1,860,867 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 123 means multiplying 123 by itself three times: 123 × 123 = 15,129, and then 15,129 × 123 = 1,860,867.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 1,860,867 cm³.
Problem 5
Estimate the cube 122.9 using the cube 123.
The cube of 122.9 is approximately 1,860,867.
Explanation
First, identify the cube of 123.
The cube of 123 is 123³ = 1,860,867. Since 122.9 is only a tiny bit less than 123, the cube of 122.9 will be almost the same as the cube of 123.
The cube of 122.9 is approximately 1,860,867 because the difference between 122.9 and 123 is very small.
So, we can approximate the value as 1,860,867.
FAQs on Cube of 123
1.What are the perfect cubes up to 123?
2.How do you calculate 123³?
3.What is the meaning of 123³?
4.What is the cube root of 123?
5.Is 123 a perfect cube?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Cube of 123?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Cube of 123?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for Cube of 123
- 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 to obtain a product.
- 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.
- Volume of a Cube: The amount of space occupied by a cube, calculated as side length cubed (Side³).
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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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