Last updated on June 1st, 2025
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing the sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 421.
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 421 can be written as 421³, which is the exponential form.
Or it can also be written in arithmetic form as 421 × 421 × 421.
In order to check whether a number is a cube number or not, we can use the following three methods: the multiplication method, a factor formula (a³), or by using a calculator. These three methods will help kids to cube 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. 421³ = 421 × 421 × 421
Step 2: You get 74,792,761 as the answer. Hence, the cube of 421 is 74,792,761.
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 421 into two parts. Let a = 420 and b = 1, so a + b = 421
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term: a³ = 420³ 3a²b = 3 × 420² × 1 3ab² = 3 × 420 × 1² b³ = 1³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (420 + 1)³ = 420³ + 3 × 420² × 1 + 3 × 420 × 1² + 1³ 421³ = 74,088,000 + 529,200 + 1,260 + 1 421³ = 74,792,761
Step 5: Hence, the cube of 421 is 74,792,761.
To find the cube of 421 using a calculator, input the number 421 and use the cube function (if available) or multiply 421 × 421 × 421. This operation calculates the value of 421³, resulting in 74,792,761. 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 2, then 1.
Step 3: If the calculator has a cube function, press it to calculate 421³.
Step 4: If there is no cube function on the calculator, simply multiply 421 three times manually.
Step 5: The calculator will display 74,792,761.
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 421?
The cube of 421 is 74,792,761 and the cube root of 421 is approximately 7.488.
First, let’s find the cube of 421.
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 421³ = 74,792,761. Next, we must find the cube root of 421.
We know that the cube root of a number 'x', such that ∛x = y
where x is the given number, and y is the cube root value of the number.
So, we get ∛421 ≈ 7.488.
Hence, the cube of 421 is 74,792,761 and the cube root of 421 is approximately 7.488.
If the side length of the cube is 421 cm, what is the volume?
The volume is 74,792,761 cm³.
Use the volume formula for a cube V = Side³.
Substitute 421 for the side length: V = 421³ = 74,792,761 cm³.
How much larger is 421³ than 411³?
421³ – 411³ = 9,487,761.
First, find the cube of 421, which is 74,792,761.
Next, find the cube of 411, which is 65,305,000.
Now, find the difference between them using the subtraction method. 74,792,761 – 65,305,000 = 9,487,761.
Therefore, 421³ is 9,487,761 larger than 411³.
If a cube with a side length of 421 cm is compared to a cube with a side length of 21 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 421 cm is 74,792,761 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 421 means multiplying 421 by itself three times: 421 × 421 = 177,241, and then 177,241 × 421 = 74,792,761.
The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.
Therefore, the volume of the cube is 74,792,761 cm³.
Estimate the cube of 420.1 using the cube of 421.
The cube of 420.1 is approximately 74,792,761.
First, identify the cube of 421, The cube of 421 is 421³ = 74,792,761.
Since 420.1 is only a tiny bit less than 421, the cube of 420.1 will be almost the same as the cube of 421.
The cube of 420.1 is approximately 74,792,761 because the difference between 420.1 and 421 is very small.
So, we can approximate the value as 74,792,761.
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.