101 LearnersLast updated on May 26th, 2025
Cube of 498
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 498.
Cube of 498
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 498 can be written as 498³, which is the exponential form. Or it can also be written in arithmetic form as 498 × 498 × 498.
How to Calculate the Value of Cube of 498
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. 498³ = 498 × 498 × 498
Step 2: You get 123,502,392 as the answer. Hence, the cube of 498 is 123,502,392.
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 498 into two parts, as 400 and 98. Let a = 400 and b = 98, so a + b = 498
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 400³
3a²b = 3 × 400² × 98
3ab² = 3 × 400 × 98²
b³ = 98³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³
(400 + 98)³ = 400³ + 3 × 400² × 98 + 3 × 400 × 98² + 98³
498³ = 64,000,000 + 47,040,000 + 11,520,000 + 941,392
498³ = 123,502,392
Step 5: Hence, the cube of 498 is 123,502,392.
Using a Calculator
To find the cube of 498 using a calculator, input the number 498 and use the cube function (if available) or multiply 498 × 498 × 498. This operation calculates the value of 498³, resulting in 123,502,392. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 4, 9, 8
Step 3: If the calculator has a cube function, press it to calculate 498³.
Step 4: If there is no cube function on the calculator, simply multiply 498 three times manually.
Step 5: The calculator will display 123,502,392.
Tips and Tricks for the Cube of 498
- 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 498
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, 498 × 498 and not 498 × 498 × 498. Always remember that 498³ = 498 × 498 × 498.
Solved Examples on Cube of 498
Problem 1
What is the cube and cube root of 498?
The cube of 498 is 123,502,392 and the cube root of 498 is approximately 7.937.
Explanation
First, let’s find the cube of 498. 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 498³ = 123,502,392
Next, we must find the cube root of 498 We know that the cube root of a number ‘x’, such that ³√x = y Where ‘x’ is the given number, and y is the cube root value of the number
So, we get ³√498 ≈ 7.937
Hence the cube of 498 is 123,502,392 and the cube root of 498 is approximately 7.937.
Problem 2
If the side length of the cube is 498 cm, what is the volume?
The volume is 123,502,392 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 498 for the side length: V = 498³ = 123,502,392 cm³.
Problem 3
How much larger is 498³ than 400³?
498³ – 400³ = 59,502,392.
Explanation
First, find the cube of 498³, which is 123,502,392
Next, find the cube of 400³, which is 64,000,000
Now, find the difference between them using the subtraction method.
123,502,392 – 64,000,000 = 59,502,392
Therefore, 498³ is 59,502,392 larger than 400³.
Problem 4
If a cube with a side length of 498 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 498 cm is 123,502,392 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 498 means multiplying 498 by itself three times: 498 × 498 = 248,004, and then 248,004 × 498 = 123,502,392.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 123,502,392 cm³.
Problem 5
Estimate the cube of 497.5 using the cube of 498.
The cube of 497.5 is approximately 123,502,392.
Explanation
First, identify the cube of 498, The cube of 498 is 498³ = 123,502,392.
Since 497.5 is only a tiny bit less than 498, the cube of 497.5 will be almost the same as the cube of 498.
The cube of 497.5 is approximately 123,502,392 because the difference between 497.5 and 498 is very small.
So, we can approximate the value as 123,502,392.
FAQs on Cube of 498
1.What are the perfect cubes up to 498?
2.How do you calculate 498³?
3.What is the meaning of 498³?
4.What is the cube root of 498?
5.Is 498 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 498?
8.How do technology and digital tools in Oman support learning Algebra and Cube of 498?
9.Does learning Algebra support future career opportunities for students in Oman?
Important Glossaries for Cube of 498
- 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 three equal integers.
- Volume of a Cube: The amount of space inside a cube, calculated as the cube of the side length.
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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.
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