118 LearnersLast updated on May 30th, 2025
Cube of 89
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 the cube of 89.
Cube of 89
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 89 can be written as 89³, which is the exponential form.
Or it can also be written in arithmetic form as, 89 × 89 × 89.
How to Calculate the Value of Cube of 89
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 (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. 89³ = 89 × 89 × 89
Step 2: You get 704,969 as the answer.
Hence, the cube of 89 is 704,969.
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 89 into two parts, as 80 and 9. Let a = 80 and b = 9, so a + b = 89
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 80³ 3a²b = 3 × 80² × 9 3ab² = 3 × 80 × 9² b³ = 9³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (80 + 9)³ = 80³ + 3 × 80² × 9 + 3 × 80 × 9² + 9³ 89³ = 512,000 + 172,800 + 19,440 + 729 89³ = 704,969
Step 5: Hence, the cube of 89 is 704,969.
Using a Calculator
To find the cube of 89 using a calculator, input the number 89 and use the cube function (if available) or multiply 89 × 89 × 89. This operation calculates the value of 89³, resulting in 704,969. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 8 followed by 9
Step 3: If the calculator has a cube function, press it to calculate 89³.
Step 4: If there is no cube function on the calculator, simply multiply 89 three times manually.
Step 5: The calculator will display 704,969.
Tips and Tricks for the Cube of 89
- 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 89
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, 89 × 89 and not 89 × 89 × 89. Always remember that 89³ = 89 × 89 × 89.
Solved Examples on Cube of 89
Problem 1
What is the cube and cube root of 89?
The cube of 89 is 704,969 and the cube root of 89 is approximately 4.464.
Explanation
First, let’s find the cube of 89.
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 89³ = 704,969 Next, we must find the cube root of 89.
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 ∛89 ≈ 4.464
Hence, the cube of 89 is 704,969 and the cube root of 89 is approximately 4.464.
Problem 2
If the side length of the cube is 89 cm, what is the volume?
The volume is 704,969 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 89 for the side length: V = 89³ = 704,969 cm³.
Problem 3
How much larger is 89³ than 79³?
89³ – 79³ = 347,989.
Explanation
First, find the cube of 89³, that is 704,969.
Next, find the cube of 79³, which is 356,980.
Now, find the difference between them using the subtraction method. 704,969 – 356,980 = 347,989
Therefore, the 89³ is 347,989 larger than 79³.
Problem 4
If a cube with a side length of 89 cm is compared to a cube with a side length of 45 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 89 cm is 704,969 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 89 means multiplying 89 by itself three times: 89 × 89 = 7,921, and then 7,921 × 89 = 704,969.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 704,969 cm³.
Problem 5
Estimate the cube of 88.9 using the cube of 89.
The cube of 88.9 is approximately 704,969.
Explanation
First, identify the cube of 89,
The cube of 89 is 89³ = 704,969.
Since 88.9 is only a tiny bit less than 89, the cube of 88.9 will be almost the same as the cube of 89.
The cube of 88.9 is approximately 704,969 because the difference between 88.9 and 89 is very small.
So, we can approximate the value as 704,969.
FAQs on Cube of 89
1.What are the perfect cubes up to 89?
2.How do you calculate 89³?
3.What is the meaning of 89³?
4.What is the cube root of 89?
5.Is 89 a perfect cube?
6.How does learning Algebra help students in Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Cube of 89?
8.How do technology and digital tools in Indonesia support learning Algebra and Cube of 89?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for Cube of 89
- 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.
- Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
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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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