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 when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 428.
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 428 can be written as 428³, which is the exponential form.
Or it can also be written in arithmetic form as 428 × 428 × 428.
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 methods will help 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. 428³ = 428 × 428 × 428
Step 2: You get 78,402,752 as the answer. Hence, the cube of 428 is 78,402,752.
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 428 into two parts. Let a = 400 and b = 28, so a + b = 428
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × 28 3ab² = 3 × 400 × 28² b³ = 28³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 + 28)³ = 400³ + 3 × 400² × 28 + 3 × 400 × 28² + 28³ 428³ = 64,000,000 + 13,440,000 + 1,344,000 + 21,952 428³ = 78,402,752
Step 5: Hence, the cube of 428 is 78,402,752.
To find the cube of 428 using a calculator, input the number 428 and use the cube function (if available) or multiply 428 × 428 × 428. This operation calculates the value of 428³, resulting in 78,402,752. 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 8
Step 3: If the calculator has a cube function, press it to calculate 428³.
Step 4: If there is no cube function on the calculator, simply multiply 428 three times manually.
Step 5: The calculator will display 78,402,752.
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 might occur during the process of cubing a number. Let us take a look at five of the major mistakes that might occur:
What is the cube and cube root of 428?
The cube of 428 is 78,402,752 and the cube root of 428 is approximately 7.53.
First, let’s find the cube of 428.
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 428³ = 78,402,752 Next, we must find the cube root of 428
We know that the cube root of a number ‘x’, such that ³√x = y
Where ‘x’ is the given number, and y is the cube root value of the number
So, we get ³√428 ≈ 7.53
Hence the cube of 428 is 78,402,752 and the cube root of 428 is approximately 7.53.
If the side length of the cube is 428 cm, what is the volume?
The volume is 78,402,752 cm³.
Use the volume formula for a cube V = Side³.
Substitute 428 for the side length: V = 428³ = 78,402,752 cm³.
How much larger is 428³ than 400³?
428³ – 400³ = 14,402,752.
First find the cube of 428, which is 78,402,752
Next, find the cube of 400, which is 64,000,000
Now, find the difference between them using the subtraction method. 78,402,752 – 64,000,000 = 14,402,752
Therefore, 428³ is 14,402,752 larger than 400³.
If a cube with a side length of 428 cm is compared to a cube with a side length of 28 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 428 cm is 78,402,752 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a three-dimensional object).
Cubing 428 means multiplying 428 by itself three times: 428 × 428 = 183,184, and 183,184 × 428 = 78,402,752.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 78,402,752 cm³.
Estimate the cube 427.9 using the cube 428.
The cube of 427.9 is approximately 78,402,752.
First, identify the cube of 428, The cube of 428 is 428³ = 78,402,752.
Since 427.9 is only a tiny bit less than 428, the cube of 427.9 will be almost the same as the cube of 428.
The cube of 427.9 is approximately 78,402,752 because the difference between 427.9 and 428 is very small.
So, we can approximate the value as 78,402,752.
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.