115 LearnersLast updated on May 29th, 2025
Cube of 83
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 83.
Cube of 83
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 83 can be written as 83³, which is the exponential form.
Or it can also be written in arithmetic form as, 83 × 83 × 83.
How to Calculate the Value of Cube of 83
In order 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 (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. 83³ = 83 × 83 × 83
Step 2: You get 571,787 as the answer.
Hence, the cube of 83 is 571,787.
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 83 into two parts. Let a = 80 and b = 3, so a + b = 83
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 80³ 3a²b = 3 × 80² × 3 3ab² = 3 × 80 × 3² b³ = 3³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (80 + 3)³ = 80³ + 3 × 80² × 3 + 3 × 80 × 3² + 3³ 83³ = 512,000 + 57,600 + 2,160 + 27 83³ = 571,787
Step 5: Hence, the cube of 83 is 571,787.
Using a Calculator
To find the cube of 83 using a calculator, input the number 83 and use the cube function (if available) or multiply 83 × 83 × 83. This operation calculates the value of 83³, resulting in 571,787. 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 3
Step 3: If the calculator has a cube function, press it to calculate 83³.
Step 4: If there is no cube function on the calculator, simply multiply 83 three times manually.
Step 5: The calculator will display 571,787.
Tips and Tricks for the Cube of 83
- 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 83
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, 83 × 83 and not 83 × 83 × 83. Always remember that 83³ = 83 × 83 × 83.
Solved Examples on Cube of 83
Problem 1
What is the cube and cube root of 83?
The cube of 83 is 571,787 and the cube root of 83 is approximately 4.341.
Explanation
First, let’s find the cube of 83.
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 83³ = 571,787 Next, we must find the cube root of 83
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 ∛83 ≈ 4.341
Hence the cube of 83 is 571,787 and the cube root of 83 is approximately 4.341.
Problem 2
If the side length of the cube is 83 cm, what is the volume?
The volume is 571,787 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 83 for the side length: V = 83³ = 571,787 cm³.
Problem 3
How much larger is 83³ than 80³?
83³ – 80³ = 59,787.
Explanation
First, find the cube of 83³, that is 571,787
Next, find the cube of 80³, which is 512,000
Now, find the difference between them using the subtraction method. 571,787 – 512,000 = 59,787
Therefore, 83³ is 59,787 larger than 80³.
Problem 4
If a cube with a side length of 83 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 83 cm is 571,787 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 83 means multiplying 83 by itself three times: 83 × 83 = 6,889, and then 6,889 × 83 = 571,787.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 571,787 cm³.
Problem 5
Estimate the cube of 82.9 using the cube of 83.
The cube of 82.9 is approximately 571,787.
Explanation
First, identify the cube of 83,
The cube of 83 is 83³ = 571,787. Since 82.9 is only a tiny bit less than 83, the cube of 82.9 will be almost the same as the cube of 83.
The cube of 82.9 is approximately 571,787 because the difference between 82.9 and 83 is very small.
So, we can approximate the value as 571,787.
FAQs on Cube of 83
1.What are the perfect cubes up to 83?
2.How do you calculate 83³?
3.What is the meaning of 83³?
4.What is the cube root of 83?
5.Is 83 a perfect cube?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Cube of 83?
8.How do technology and digital tools in United Kingdom support learning Algebra and Cube of 83?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for Cube of 83
- Binomial Formula: 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: 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: Calculated as the side length raised to the power of three, expressed as 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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