116 LearnersLast updated on May 29th, 2025
Cube of 82
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing the sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 82.
Cube of 82
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 82 can be written as 82³, which is the exponential form.
Or it can also be written in arithmetic form as, 82 × 82 × 82.
How to Calculate the Value of Cube of 82
In order to check whether a number is a cube number or not, we can use the following three methods: 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 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. 82³ = 82 × 82 × 82
Step 2: You get 551,368 as the answer.
Hence, the cube of 82 is 551,368.
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 82 into two parts, such as 80 and 2. Let a = 80 and b = 2, so a + b = 82
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 80³ 3a²b = 3 × 80² × 2 3ab² = 3 × 80 × 2² b³ = 2³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (80 + 2)³ = 80³ + 3 × 80² × 2 + 3 × 80 × 2² + 2³ 82³ = 512,000 + 38,400 + 960 + 8 82³ = 551,368
Step 5: Hence, the cube of 82 is 551,368.
Using a Calculator
To find the cube of 82 using a calculator, input the number 82 and use the cube function (if available) or multiply 82 × 82 × 82. This operation calculates the value of 82³, resulting in 551,368. 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 2.
Step 3: If the calculator has a cube function, press it to calculate 82³.
Step 4: If there is no cube function on the calculator, simply multiply 82 three times manually.
Step 5: The calculator will display 551,368.
Tips and Tricks for the Cube of 82
- 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 82
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, 82 × 82 and not 82 × 82 × 82. Always remember that 82³ = 82 × 82 × 82.
Solved Examples on Cube of 82
Problem 1
What is the cube and cube root of 82?
The cube of 82 is 551,368 and the cube root of 82 is approximately 4.326.
Explanation
First, let’s find the cube of 82.
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 82³ = 551,368 Next, we must find the cube root of 82
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 ∛82 ≈ 4.326
Hence the cube of 82 is 551,368 and the cube root of 82 is approximately 4.326.
Problem 2
If the side length of the cube is 82 cm, what is the volume?
The volume is 551,368 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 82 for the side length: V = 82³ = 551,368 cm³.
Problem 3
How much larger is 82³ than 42³?
82³ – 42³ = 511,048.
Explanation
First find the cube of 82³, which is 551,368
Next, find the cube of 42³, which is 74,088
Now, find the difference between them using the subtraction method. 551,368 – 74,088 = 477,280
Therefore, 82³ is 477,280 larger than 42³.
Problem 4
If a cube with a side length of 82 cm is compared to a cube with a side length of 22 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 82 cm is 551,368 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 82 means multiplying 82 by itself three times: 82 × 82 = 6,724, and then 6,724 × 82 = 551,368.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 551,368 cm³.
Problem 5
Estimate the cube of 81.9 using the cube of 82.
The cube of 81.9 is approximately 551,368.
Explanation
First, identify the cube of 82,
The cube of 82 is 82³ = 551,368.
Since 81.9 is only a tiny bit less than 82, the cube of 81.9 will be almost the same as the cube of 82.
The cube of 81.9 is approximately 551,368 because the difference between 81.9 and 82 is very small.
So, we can approximate the value as 551,368.
FAQs on Cube of 82
1.What are the perfect cubes up to 82?
2.How do you calculate 82³?
3.What is the meaning of 82³?
4.What is the cube root of 82?
5.Is 82 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 82?
8.How do technology and digital tools in Thailand support learning Algebra and Cube of 82?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for Cube of 82
- 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.
- Volume: The amount of space occupied by a 3-dimensional object, calculated for a cube as Side³.
- Perfect Cube: A number that can be expressed as the cube of an integer.
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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.
