Last updated on May 30th, 2025
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.
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.
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.
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.
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.
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.
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.
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:
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.
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.
If the side length of a cube is 404 cm, what is the volume?
The volume is 65,975,264 cm³.
Use the volume formula for a cube V = Side³.
Substitute 404 for the side length: V = 404³ = 65,975,264 cm³.
How much larger is 404³ than 304³?
404³ – 304³ = 49,865,664.
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.
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.
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.
Estimate the cube of 403 using the cube of 404.
The cube of 403 is approximately 65,975,264.
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.
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.
: He loves to play the quiz with kids through algebra to make kids love it.