100 LearnersLast updated on June 3rd, 2025
Cube of 289
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 289.
Cube of 289
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 multiplying a negative number by itself three times results in a negative number.
The cube of 289 can be written as 289³, which is the exponential form.
Or it can also be written in arithmetic form as, 289 × 289 × 289.
How to Calculate the Value of Cube of 289
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
- 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. 289³ = 289 × 289 × 289
Step 2: You get 24,089,321 as the answer. Hence, the cube of 289 is 24,089,321.
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 289 into two parts, as a and b. Let a = 280 and b = 9, so a + b = 289
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 280³ 3a²b = 3 × 280² × 9 3ab² = 3 × 280 × 9² b³ = 9³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (280 + 9)³ = 280³ + 3 × 280² × 9 + 3 × 280 × 9² + 9³ 289³ = 21,952,000 + 211,680 + 68,040 + 729 289³ = 24,089,321
Step 5: Hence, the cube of 289 is 24,089,321.
Using a Calculator
To find the cube of 289 using a calculator, input the number 289 and use the cube function (if available) or multiply 289 × 289 × 289. This operation calculates the value of 289³, resulting in 24,089,321. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Input 289
Step 3: If the calculator has a cube function, press it to calculate 289³.
Step 4: If there is no cube function on the calculator, simply multiply 289 three times manually.
Step 5: The calculator will display 24,089,321.
Tips and Tricks for the Cube of 289
- 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 289
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, 289 × 289 and not 289 × 289 × 289. Always remember that 289³ = 289 × 289 × 289.
Solved Examples on Cube of 289
Problem 1
What is the cube and cube root of 289?
The cube of 289 is 24,089,321 and the cube root of 289 is approximately 6.640.
Explanation
First, let’s find the cube of 289.
We know that the cube of a number is such that x³ = y
Where x is the given number, and y is the cubed value of that number.
So, we get 289³ = 24,089,321. Next, we must find the cube root of 289.
We know that the cube root of a number ‘x’, is 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√289 ≈ 6.640.
Hence, the cube of 289 is 24,089,321 and the cube root of 289 is approximately 6.640.
Problem 2
If the side length of a cube is 289 cm, what is the volume?
The volume is 24,089,321 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 289 for the side length: V = 289³ = 24,089,321 cm³.
Problem 3
How much larger is 289³ than 199³?
289³ – 199³ = 16,815,640.
Explanation
First, find the cube of 289³, which is 24,089,321.
Next, find the cube of 199³, which is 7,273,681.
Now, find the difference between them using the subtraction method. 24,089,321 – 7,273,681 = 16,815,640.
Therefore, 289³ is 16,815,640 larger than 199³.
Problem 4
If a cube with a side length of 289 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 289 cm is 24,089,321 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 289 means multiplying 289 by itself three times: 289 × 289 = 83,521, and then 83,521 × 289 = 24,089,321.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 24,089,321 cm³.
Problem 5
Estimate the cube of 288.9 using the cube of 289.
The cube of 288.9 is approximately 24,089,321.
Explanation
First, identify the cube of 289,
The cube of 289 is 289³ = 24,089,321.
Since 288.9 is only a tiny bit less than 289, the cube of 288.9 will be almost the same as the cube of 289.
The cube of 288.9 is approximately 24,089,321 because the difference between 288.9 and 289 is very small.
So, we can approximate the value as 24,089,321.
FAQs on Cube of 289
1.What are the perfect cubes up to 289?
2.How do you calculate 289³?
3.What is the meaning of 289³?
4.What is the cube root of 289?
5.Is 289 a perfect cube?
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Cube of 289?
8.How do technology and digital tools in Thailand support learning Algebra and Cube of 289?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for Cube of 289
- 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.
- Volume of a Cube: The amount of space occupied by a cube, calculated using the formula V = 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.
