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 sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 422.
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 422 can be written as 422³, which is the exponential form.
Or it can also be written in arithmetic form as, 422 × 422 × 422.
To check whether a number is a cube number or not, you can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These methods will help you 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. 422³ = 422 × 422 × 422
Step 2: You get 75,307,048 as the answer. Hence, the cube of 422 is 75,307,048.
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 422 into two parts, as 400 and 22. Let a = 400 and b = 22, so a + b = 422
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × 22 3ab² = 3 × 400 × 22² b³ = 22³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 + 22)³ = 400³ + 3 × 400² × 22 + 3 × 400 × 22² + 22³ 422³ = 64,000,000 + 10,560,000 + 3,872,000 + 10,648 422³ = 75,307,048
Step 5: Hence, the cube of 422 is 75,307,048.
To find the cube of 422 using a calculator, input the number 422 and use the cube function (if available) or multiply 422 × 422 × 422. This operation calculates the value of 422³, resulting in 75,307,048. 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 again 2
Step 3: If the calculator has a cube function, press it to calculate 422³.
Step 4: If there is no cube function on the calculator, simply multiply 422 three times manually.
Step 5: The calculator will display 75,307,048.
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 happen:
What is the cube and cube root of 422?
The cube of 422 is 75,307,048, and the cube root of 422 is approximately 7.506.
First, let’s find the cube of 422.
We know that the 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 422³ = 75,307,048. Next, we must find the cube root of 422.
We know that the 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 ∛422 ≈ 7.506.
Hence, the cube of 422 is 75,307,048, and the cube root of 422 is approximately 7.506.
If the side length of the cube is 422 cm, what is the volume?
The volume is 75,307,048 cm³.
Use the volume formula for a cube V = Side³.
Substitute 422 for the side length: V = 422³ = 75,307,048 cm³.
How much larger is 422³ than 400³?
422³ – 400³ = 11,307,048.
First, find the cube of 422, which is 75,307,048.
Next, find the cube of 400, which is 64,000,000.
Now, find the difference between them using the subtraction method. 75,307,048 – 64,000,000 = 11,307,048.
Therefore, 422³ is 11,307,048 larger than 400³.
If a cube with a side length of 422 cm is compared to a cube with a side length of 22 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 422 cm is 75,307,048 cm³, which is significantly larger.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 422 means multiplying 422 by itself three times: 422 × 422 = 178,084, and then 178,084 × 422 = 75,307,048.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 75,307,048 cm³.
Estimate the cube of 421.9 using the cube of 422.
The cube of 421.9 is approximately 75,307,048.
First, identify the cube of 422. The cube of 422 is 422³ = 75,307,048.
Since 421.9 is only a tiny bit less than 422, the cube of 421.9 will be almost the same as the cube of 422.
The cube of 421.9 is approximately 75,307,048 because the difference between 421.9 and 422 is very small.
So, we can approximate the value as 75,307,048.
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.