Last updated on May 30th, 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 412.
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 by itself three times results in a negative number.
The cube of 412 can be written as 412³, which is the exponential form.
Or it can also be written in arithmetic form as, 412 × 412 × 412.
In order to check whether a number is a cube number or not, we can use the following three methods, such as 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 numbers 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. 412³ = 412 × 412 × 412
Step 2: You get 69,922,688 as the answer. Hence, the cube of 412 is 69,922,688.
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 412 into two parts. Let a = 400 and b = 12, so a + b = 412
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × 12 3ab² = 3 × 400 × 12² b³ = 12³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 + 12)³ = 400³ + 3 × 400² × 12 + 3 × 400 × 12² + 12³ 412³ = 64,000,000 + 57,600 + 172,800 + 1,728 412³ = 69,922,688
Step 5: Hence, the cube of 412 is 69,922,688.
To find the cube of 412 using a calculator, input the number 412 and use the cube function (if available) or multiply 412 × 412 × 412. This operation calculates the value of 412³, resulting in 69,922,688. 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 1 and 2
Step 3: If the calculator has a cube function, press it to calculate 412³.
Step 4: If there is no cube function on the calculator, simply multiply 412 three times manually.
Step 5: The calculator will display 69,922,688.
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 412?
The cube of 412 is 69,922,688 and the cube root of 412 is approximately 7.438.
First, let’s find the cube of 412.
We know that 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 412³ = 69,922,688
Next, we must find the cube root of 412
We know that 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√412 ≈ 7.438
Hence the cube of 412 is 69,922,688 and the cube root of 412 is approximately 7.438.
If the side length of the cube is 412 cm, what is the volume?
The volume is 69,922,688 cm³.
Use the volume formula for a cube V = Side³.
Substitute 412 for the side length: V = 412³ = 69,922,688 cm³.
How much larger is 412³ than 400³?
412³ – 400³ = 5,922,688.
First find the cube of 412³, that is 69,922,688
Next, find the cube of 400³, which is 64,000,000
Now, find the difference between them using the subtraction method. 69,922,688 – 64,000,000 = 5,922,688
Therefore, the 412³ is 5,922,688 larger than 400³.
If a cube with a side length of 412 cm is compared to a cube with a side length of 200 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 412 cm is 69,922,688 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 412 means multiplying 412 by itself three times: 412 × 412 = 169,744, and then 169,744 × 412 = 69,922,688.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 69,922,688 cm³.
Estimate the cube 411.9 using the cube 412.
The cube of 411.9 is approximately 69,922,688.
First, identify the cube of 412
The cube of 412 is 412³ = 69,922,688.
Since 411.9 is only a tiny bit less than 412, the cube of 411.9 will be almost the same as the cube of 412.
The cube of 411.9 is approximately 69,922,688 because the difference between 411.9 and 412 is very small.
So, we can approximate the value as 69,922,688.
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.