101 LearnersLast updated on May 26th, 2025
Cube of 500
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 500.
Cube of 500
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 500 can be written as 500³, which is the exponential form. Or it can also be written in arithmetic form as, 500 × 500 × 500.
How to Calculate the Value of Cube of 500
In order to check whether a number is a cube number or not, we can use the following three methods, such as 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. 500³ = 500 × 500 × 500
Step 2: You get 125,000,000 as the answer. Hence, the cube of 500 is 125,000,000.
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 500 into two parts, as and . Let a = 400 and b = 100, so a + b = 500
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × 100 3ab² = 3 × 400 × 100² b³ = 100³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(400 + 100)³ = 400³ + 3 × 400² × 100 + 3 × 400 × 100² + 100³
500³ = 64,000,000 + 48,000,000 + 12,000,000 + 1,000,000
500³ = 125,000,000
Step 5: Hence, the cube of 500 is 125,000,000.
Using a Calculator
To find the cube of 500 using a calculator, input the number 500 and use the cube function (if available) or multiply 500 × 500 × 500. This operation calculates the value of 500³, resulting in 125,000,000. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 5 followed by 0 twice
Step 3: If the calculator has a cube function, press it to calculate 500³.
Step 4: If there is no cube function on the calculator, simply multiply 500 three times manually.
Step 5: The calculator will display 125,000,000.
Tips and Tricks for the Cube of 500
- 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 500
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, 500 × 500 and not 500 × 500 × 500. Always remember that 500³ = 500 × 500 × 500.
Solved Examples on Cube of 500
Problem 1
What is the cube and cube root of 500?
The cube of 500 is 125,000,000 and the cube root of 500 is approximately 7.937.
Explanation
First, let’s find the cube of 500.
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 500³ = 125,000,000
Next, we must find the cube root of 500 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 ∛500 ≈ 7.937
Hence the cube of 500 is 125,000,000 and the cube root of 500 is approximately 7.937.
Problem 2
If the side length of a cube is 500 cm, what is the volume?
The volume is 125,000,000 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 500 for the side length: V = 500³ = 125,000,000 cm³.
Problem 3
How much larger is 500³ than 400³?
500³ – 400³ = 61,000,000.
Explanation
First, find the cube of 500³, that is 125,000,000
Next, find the cube of 400³, which is 64,000,000
Now, find the difference between them using the subtraction method.
125,000,000 – 64,000,000 = 61,000,000
Therefore, 500³ is 61,000,000 larger than 400³.
Problem 4
If a cube with a side length of 500 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 500 cm is 125,000,000 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 500 means multiplying 500 by itself three times: 500 × 500 = 250,000, and then 250,000 × 500 = 125,000,000.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 125,000,000 cm³.
Problem 5
Estimate the cube of 499.9 using the cube of 500.
The cube of 499.9 is approximately 125,000,000.
Explanation
First, identify the cube of 500, The cube of 500 is 500³ = 125,000,000.
Since 499.9 is only a tiny bit less than 500, the cube of 499.9 will be almost the same as the cube of 500.
The cube of 499.9 is approximately 125,000,000
because the difference between 499.9 and 500 is very small. So, we can approximate the value as 125,000,000.
FAQs on Cube of 500
1.What are the perfect cubes up to 500?
2.How do you calculate 500³?
3.What is the meaning of 500³?
4.What is the cube root of 500?
5.Is 500 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 500?
8.How do technology and digital tools in Thailand support learning Algebra and Cube of 500?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for Cube of 500
- 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 product of an integer multiplied by itself three times.
- Volume of a Cube: The amount of space occupied by a cube, calculated as the side length cubed (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
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