114 LearnersLast updated on May 30th, 2025
Cube of 538
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 538.
Cube of 538
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 538 can be written as 538³, which is the exponential form.
Or it can also be written in arithmetic form as, 538 × 538 × 538.
How to Calculate the Value of Cube of 538
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 (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. 538³ = 538 × 538 × 538
Step 2: You get 155,947,352 as the answer. Hence, the cube of 538 is 155,947,352.
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 538 into two parts, as 500 and 38. Let a = 500 and b = 38, so a + b = 538
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 500³ 3a²b = 3 × 500² × 38 3ab² = 3 × 500 × 38² b³ = 38³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (500 + 38)³ = 500³ + 3 × 500² × 38 + 3 × 500 × 38² + 38³ 538³ = 125,000,000 + 28,500,000 + 21,660,000 + 54,872 538³ = 155,947,352
Step 5: Hence, the cube of 538 is 155,947,352.
Using a Calculator
To find the cube of 538 using a calculator, input the number 538 and use the cube function (if available) or multiply 538 × 538 × 538. This operation calculates the value of 538³, resulting in 155,947,352. 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 3 and then 8
Step 3: If the calculator has a cube function, press it to calculate 538³.
Step 4: If there is no cube function on the calculator, simply multiply 538 three times manually.
Step 5: The calculator will display 155,947,352.
Tips and Tricks for the Cube of 538
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 538
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, 538 × 538 and not 538 × 538 × 538. Always remember that 538³ = 538 × 538 × 538.
Solved Examples on Cube of 538
Problem 1
What is the cube and cube root of 538?
The cube of 538 is 155,947,352 and the cube root of 538 is approximately 8.143.
Explanation
First, let’s find the cube of 538.
We know that the cube of a number is calculated as x³ = y
Where x is the given number, and y is the cubed value of that number.
So, we get 538³ = 155,947,352. Next, we must find the cube root of 538.
We know that the cube root of a number ‘x’ is calculated as ∛x = y
Where ‘x’ is the given number, and y is the cube root value of the number.
So, we get ∛538 ≈ 8.143.
Hence the cube of 538 is 155,947,352 and the cube root of 538 is approximately 8.143.
Problem 2
If the side length of a cube is 538 cm, what is the volume?
The volume is 155,947,352 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 538 for the side length: V = 538³ = 155,947,352 cm³.
Problem 3
How much larger is 538³ than 500³?
538³ – 500³ = 30,947,352.
Explanation
First find the cube of 538, which is 155,947,352.
Next, find the cube of 500, which is 125,000,000.
Now, find the difference between them using the subtraction method. 155,947,352 – 125,000,000 = 30,947,352.
Therefore, 538³ is 30,947,352 larger than 500³.
Problem 4
If a cube with a side length of 538 cm is compared to a cube with a side length of 50 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 538 cm is 155,947,352 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 538 means multiplying 538 by itself three times: 538 × 538 = 289,444, and then 289,444 × 538 = 155,947,352.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 155,947,352 cm³.
Problem 5
Estimate the cube of 537.9 using the cube of 538.
The cube of 537.9 is approximately 155,947,352.
Explanation
First, identify the cube of 538, The cube of 538 is 538³ = 155,947,352.
Since 537.9 is only a tiny bit less than 538, the cube of 537.9 will be almost the same as the cube of 538.
The cube of 537.9 is approximately 155,947,352 because the difference between 537.9 and 538 is very small.
So, we can approximate the value as 155,947,352.
FAQs on Cube of 538
1.What are the perfect cubes up to 538?
2.How do you calculate 538³?
3.What is the meaning of 538³?
4.What is the cube root of 538?
5.Is 538 a perfect cube?
6.How does learning Algebra help students in Oman make better decisions in daily life?
7.How can cultural or local activities in Oman support learning Algebra topics such as Cube of 538?
8.How do technology and digital tools in Oman support learning Algebra and Cube of 538?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for Cube of 538
- 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: A number which, when used three times in a multiplication, gives the original number. For example, the cube root of 27 is 3.
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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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