114 LearnersLast updated on May 30th, 2025
Cube of 398
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 398.
Cube of 398
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 398 can be written as 398³, which is the exponential form.
Or it can also be written in arithmetic form as 398 × 398 × 398.
How to Calculate the Value of Cube of 398
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 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. 398³ = 398 × 398 × 398
Step 2: You get 63,113,992 as the answer. Hence, the cube of 398 is 63,113,992.
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 398 into two parts, as a and b. Let a = 390 and b = 8, so a + b = 398
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 390³ 3a²b = 3 × 390² × 8 3ab² = 3 × 390 × 8² b³ = 8³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (390 + 8)³ = 390³ + 3 × 390² × 8 + 3 × 390 × 8² + 8³ 398³ = 59,319,000 + 36,504 + 7,488 + 512 398³ = 63,113,992
Step 5: Hence, the cube of 398 is 63,113,992.
Using a Calculator
To find the cube of 398 using a calculator, input the number 398 and use the cube function (if available) or multiply 398 × 398 × 398. This operation calculates the value of 398³, resulting in 63,113,992. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 3 followed by 9 and 8
Step 3: If the calculator has a cube function, press it to calculate 398³.
Step 4: If there is no cube function on the calculator, simply multiply 398 three times manually.
Step 5: The calculator will display 63,113,992.
Tips and Tricks for the Cube of 398
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 398
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, 398 × 398 and not 398 × 398 × 398. Always remember that 398³ = 398 × 398 × 398.
Solved Examples on Cube of 398
Problem 1
What is the cube and cube root of 398?
The cube of 398 is 63,113,992 and the cube root of 398 is approximately 7.368.
Explanation
First, let’s find the cube of 398.
We know that the cube of a number is such that x³ = y
where x is the given number, and y is the cubed value of that number.
So, we get 398³ = 63,113,992. Next, we must find the cube root of 398.
We know that the cube root of a number ‘x’ is such that ∛x = y
where ‘x’ is the given number, and y is the cube root value of the number.
So, we get ∛398 ≈ 7.368.
Hence the cube of 398 is 63,113,992 and the cube root of 398 is approximately 7.368.
Problem 2
If the side length of the cube is 398 cm, what is the volume?
The volume is 63,113,992 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 398 for the side length: V = 398³ = 63,113,992 cm³.
Problem 3
How much larger is 398³ than 298³?
398³ – 298³ = 59,395,728.
Explanation
First, find the cube of 398³, which is 63,113,992.
Next, find the cube of 298³, which is 3,718,264.
Now, find the difference between them using the subtraction method. 63,113,992 – 3,718,264 = 59,395,728.
Therefore, 398³ is 59,395,728 larger than 298³.
Problem 4
If a cube with a side length of 398 cm is compared to a cube with a side length of 98 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 398 cm is 63,113,992 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 398 means multiplying 398 by itself three times: 398 × 398 = 158,404, and then 158,404 × 398 = 63,113,992.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 63,113,992 cm³.
Problem 5
Estimate the cube 397.5 using the cube 398.
The cube of 397.5 is approximately 63,113,992.
Explanation
First, identify the cube of 398. The cube of 398 is 398³ = 63,113,992.
Since 397.5 is only a tiny bit less than 398, the cube of 397.5 will be almost the same as the cube of 398.
The cube of 397.5 is approximately 63,113,992 because the difference between 397.5 and 398 is very small.
So, we can approximate the value as 63,113,992.
FAQs on Cube of 398
1.What are the perfect cubes up to 398?
2.How do you calculate 398³?
3.What is the meaning of 398³?
4.What is the cube root of 398?
5.Is 398 a perfect cube?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Cube of 398?
8.How do technology and digital tools in Singapore support learning Algebra and Cube of 398?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for Cube of 398
- 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, 3³ represents 3 × 3 × 3 equals 27.
- Multiplication Method: A fundamental mathematical process used to find the product of numbers by repeated addition.
- Perfect Cube: A number that can be expressed as the cube of an integer, such as 1, 8, 27, etc.
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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.
