117 LearnersLast updated on May 30th, 2025
Cube of 404
When a number is multiplied by itself three times, 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 404.
Cube of 404
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 multiplying a negative number by itself three times results in a negative number.
The cube of 404 can be written as 404³, which is the exponential form.
Or it can also be written in arithmetic form as, 404 × 404 × 404.
How to Calculate the Value of Cube of 404
To determine 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. 404³ = 404 × 404 × 404
Step 2: You get 65,975,464 as the answer. Hence, the cube of 404 is 65,975,464.
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 404 into two parts, as 400 and 4. Let a = 400 and b = 4, so a + b = 404
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × 4 3ab² = 3 × 400 × 4² b³ = 4³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 + 4)³ = 400³ + 3 × 400² × 4 + 3 × 400 × 4² + 4³ 404³ = 64,000,000 + 1,920,000 + 19,200 + 64 404³ = 65,975,264
Step 5: Hence, the cube of 404 is 65,975,264.
Using a Calculator
To find the cube of 404 using a calculator, input the number 404 and use the cube function (if available) or multiply 404 × 404 × 404. This operation calculates the value of 404³, resulting in 65,975,264. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 4 followed by 0 and 4
Step 3: If the calculator has a cube function, press it to calculate 404³.
Step 4: If there is no cube function on the calculator, simply multiply 404 three times manually.
Step 5: The calculator will display 65,975,264.
Tips and Tricks for the Cube of 404
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 404
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, 404 × 404 and not 404 × 404 × 404. Always remember that 404³ = 404 × 404 × 404.
Solved Examples on Cube of 404
Problem 1
What is the cube and cube root of 404?
The cube of 404 is 65,975,264 and the cube root of 404 is approximately 7.37.
Explanation
First, let’s find the cube of 404.
We know that 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 404³ = 65,975,264. Next, we must find the cube root of 404.
We know that 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 ∛404 ≈ 7.37.
Hence the cube of 404 is 65,975,264 and the cube root of 404 is approximately 7.37.
Problem 2
If the side length of a cube is 404 cm, what is the volume?
The volume is 65,975,264 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 404 for the side length: V = 404³ = 65,975,264 cm³.
Problem 3
How much larger is 404³ than 304³?
404³ – 304³ = 49,865,664.
Explanation
First, find the cube of 404, that is 65,975,264.
Next, find the cube of 304, which is 16,109,600.
Now, find the difference between them using the subtraction method. 65,975,264 – 16,109,600 = 49,865,664.
Therefore, 404³ is 49,865,664 larger than 304³.
Problem 4
If a cube with a side length of 404 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 404 cm is 65,975,264 cm³.
Explanation
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 404 means multiplying 404 by itself three times: 404 × 404 = 163,216, and then 163,216 × 404 = 65,975,264.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 65,975,264 cm³.
Problem 5
Estimate the cube of 403 using the cube of 404.
The cube of 403 is approximately 65,975,264.
Explanation
First, identify the cube of 404.
The cube of 404 is 404³ = 65,975,264.
Since 403 is only a tiny bit less than 404, the cube of 403 will be almost the same as the cube of 404.
The cube of 403 is approximately 65,975,264 because the difference between 403 and 404 is very small.
So, we can approximate the value as 65,975,264.
FAQs on Cube of 404
1.What are the perfect cubes up to 404?
2.How do you calculate 404³?
3.What is the meaning of 404³?
4.What is the cube root of 404?
5.Is 404 a perfect cube?
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Cube of 404?
8.How do technology and digital tools in Philippines support learning Algebra and Cube of 404?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for Cube of 404
- 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.
- Volume of a Cube: The amount of space occupied by a cube, calculated as side length raised to the power of three.
- Perfect Cube: A number that can be expressed as the cube of an integer.
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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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