Last updated on June 2nd, 2025
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 423.
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 423 can be written as 423³, which is the exponential form.
Or it can also be written in arithmetic form as, 423 × 423 × 423.
In order to determine whether a number is a cube number, we can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These three methods will help students 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 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. 423³ = 423 × 423 × 423
Step 2: You get 75,810,567 as the answer. Hence, the cube of 423 is 75,810,567.
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 423 into two parts, as 400 and 23. Let a = 400 and b = 23, so a + b = 423
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × 23 3ab² = 3 × 400 × 23² b³ = 23³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 + 23)³ = 400³ + 3 × 400² × 23 + 3 × 400 × 23² + 23³ 423³ = 64,000,000 + 11,040,000 + 634,800 + 12,167 423³ = 75,810,567
Step 5: Hence, the cube of 423 is 75,810,567.
To find the cube of 423 using a calculator, input the number 423 and use the cube function (if available) or multiply 423 × 423 × 423. This operation calculates the value of 423³, resulting in 75,810,567. 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 and 3
Step 3: If the calculator has a cube function, press it to calculate 423³.
Step 4: If there is no cube function on the calculator, simply multiply 423 three times manually.
Step 5: The calculator will display 75,810,567.
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 students might make during the process of cubing a number. Let us take a look at five of the major mistakes that students might make:
What is the cube and cube root of 423?
The cube of 423 is 75,810,567 and the cube root of 423 is approximately 7.508.
First, let’s find the cube of 423.
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 423³ = 75,810,567 Next, we must find the cube root of 423
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 ∛423 ≈ 7.508
Hence the cube of 423 is 75,810,567 and the cube root of 423 is approximately 7.508.
If the side length of the cube is 423 cm, what is the volume?
The volume is 75,810,567 cm³.
Use the volume formula for a cube V = Side³.
Substitute 423 for the side length: V = 423³ = 75,810,567 cm³.
How much larger is 423³ than 400³?
423³ – 400³ = 11,810,567.
First, find the cube of 423, that is 75,810,567
Next, find the cube of 400, which is 64,000,000
Now, find the difference between them using the subtraction method. 75,810,567 – 64,000,000 = 11,810,567
Therefore, 423³ is 11,810,567 larger than 400³.
If a cube with a side length of 423 cm is compared to a cube with a side length of 23 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 423 cm is 75,810,567 cm³
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 423 means multiplying 423 by itself three times: 423 × 423 = 178,929, and then 178,929 × 423 = 75,810,567.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 75,810,567 cm³.
Estimate the cube of 422.9 using the cube of 423.
The cube of 422.9 is approximately 75,810,567.
First, identify the cube of 423, The cube of 423 is 423³ = 75,810,567.
Since 422.9 is only a tiny bit less than 423, the cube of 422.9 will be almost the same as the cube of 423.
The cube of 422.9 is approximately 75,810,567 because the difference between 422.9 and 423 is very small.
So, we can approximate the value as 75,810,567.
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.