108 LearnersLast updated on 28 August 2025
Cube of 1089
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 1089.
Cube of 1089
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 1089 can be written as 1089³, which is the exponential form. Or it can also be written in arithmetic form as, 1089 × 1089 × 1089.
How to Calculate the Value of Cube of 1089
In order to check whether a number is a cube number or not, we can use the following three methods, such as:
- Multiplication Method
- Factor Formula (a³)
- 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. 1089³ = 1089 × 1089 × 1089
Step 2: You get 1,291,467,969 as the answer.
Hence, the cube of 1089 is 1,291,467,969.
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 1089 into two parts, as 1000 and 89. Let a = 1000 and b = 89, so a + b = 1089
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 1000³ 3a²b = 3 × 1000² × 89 3ab² = 3 × 1000 × 89² b³ = 89³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (1000 + 89)³ = 1000³ + 3 × 1000² × 89 + 3 × 1000 × 89² + 89³ 1089³ = 1,000,000,000 + 267,000,000 + 23,721,000 + 704,969 1089³ = 1,291,467,969
Step 5: Hence, the cube of 1089 is 1,291,467,969.
Using a Calculator
To find the cube of 1089 using a calculator, input the number 1089 and use the cube function (if available) or multiply 1089 × 1089 × 1089. This operation calculates the value of 1089³, resulting in 1,291,467,969. 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 0, 8, and 9
Step 3: If the calculator has a cube function, press it to calculate 1089³.
Step 4: If there is no cube function on the calculator, simply multiply 1089 three times manually.
Step 5: The calculator will display 1,291,467,969.
Tips and Tricks for the Cube of 1089
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 1089
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, 1089 × 1089 and not 1089 × 1089 × 1089. Always remember that 1089³ = 1089 × 1089 × 1089.
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. For this, kids should always double-check their answers.
Mistake 5
Ignoring the Binomial Formula
Kids might attempt to split 1089 into 1000 + 89, 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 1089
Problem 1
What is the cube and cube root of 1089?
The cube of 1089 is 1,291,467,969 and the cube root of 1089 is approximately 10.79.
Explanation
First, let’s find the cube of 1089.
We know that 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 1089³ = 1,291,467,969
Next, we must find the cube root of 1089 We know that 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 ∛1089 ≈ 10.79 Hence the cube of 1089 is 1,291,467,969 and the cube root of 1089 is approximately 10.79.
Problem 2
If the side length of the cube is 1089 cm, what is the volume?
The volume is 1,291,467,969 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 1089 for the side length: V = 1089³ = 1,291,467,969 cm³.
Problem 3
How much larger is 1089³ than 1000³?
1089³ – 1000³ = 291,467,969.
Explanation
First find the cube of 1089, that is 1,291,467,969
Next, find the cube of 1000, which is 1,000,000,000
Now, find the difference between them using the subtraction method. 1,291,467,969 – 1,000,000,000 = 291,467,969
Therefore, the 1089³ is 291,467,969 larger than 1000³.
Problem 4
If a cube with a side length of 1089 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 1089 cm is 1,291,467,969 cm³
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 1089 means multiplying 1089 by itself three times: 1089 × 1089 = 1,185,921, and then 1,185,921 × 1089 = 1,291,467,969.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 1,291,467,969 cm³.
Problem 5
Estimate the cube 1088.9 using the cube 1089.
The cube of 1088.9 is approximately 1,291,467,969.
Explanation
First, identify the cube of 1089
The cube of 1089 is 1089³ = 1,291,467,969.
Since 1088.9 is only a tiny bit less than 1089, the cube of 1088.9 will be almost the same as the cube of 1089.
The cube of 1088.9 is approximately 1,291,467,969 because the difference between 1088.9 and 1089 is very small.
So, we can approximate the value as 1,291,467,969.
FAQs on Cube of 1089
1.What are the perfect cubes up to 1089?
2.How do you calculate 1089³?
3.What is the meaning of 1089³?
4.What is the cube root of 1089?
5.Is 1089 a perfect cube?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Cube of 1089?
8.How do technology and digital tools in Australia support learning Algebra and Cube of 1089?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Cube of 1089
- 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.
- Cube Root: The number which, when multiplied by itself three times, gives the original number. It is denoted by the symbol ∛
- Perfect Cube: A perfect cube is a number that is the cube of an integer. For example, 8 is a perfect cube because it is 2³.
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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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