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 while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 414.
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 414 can be written as 414³, which is the exponential form.
Or it can also be written in arithmetic form as, 414 × 414 × 414.
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 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. 414³ = 414 × 414 × 414
Step 2: You get 70,878,744 as the answer. Hence, the cube of 414 is 70,878,744.
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 414 into two parts, as 400 and 14. Let a = 400 and b = 14, so a + b = 414
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 400³ 3a²b = 3 × 400² × 14 3ab² = 3 × 400 × 14² b³ = 14³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (400 + 14)³ = 400³ + 3 × 400² × 14 + 3 × 400 × 14² + 14³ 414³ = 64,000,000 + 33,600 + 235,200 + 2,744 414³ = 70,878,744
Step 5: Hence, the cube of 414 is 70,878,744.
To find the cube of 414 using a calculator, input the number 414 and use the cube function (if available) or multiply 414 × 414 × 414. This operation calculates the value of 414³, resulting in 70,878,744. 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 4.
Step 3: If the calculator has a cube function, press it to calculate 414³.
Step 4: If there is no cube function on the calculator, simply multiply 414 three times manually.
Step 5: The calculator will display 70,878,744.
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 414?
The cube of 414 is 70,878,744 and the cube root of 414 is approximately 7.457.
First, let’s find the cube of 414.
We know that the cube of a number x, such that x³ = y.
Where x is the given number, and y is the cubed value of that number.
So, we get 414³ = 70,878,744. Next, we must find the cube root of 414.
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 ∛414 = 7.457.
Hence the cube of 414 is 70,878,744 and the cube root of 414 is approximately 7.457.
If the side length of the cube is 414 cm, what is the volume?
The volume is 70,878,744 cm³.
Use the volume formula for a cube V = Side³.
Substitute 414 for the side length: V = 414³ = 70,878,744 cm³.
How much larger is 414³ than 314³?
414³ – 314³ = 50,832,560.
First, find the cube of 414³, which is 70,878,744.
Next, find the cube of 314³, which is 20,046,184.
Now, find the difference between them using the subtraction method. 70,878,744 – 20,046,184 = 50,832,560.
Therefore, 414³ is 50,832,560 larger than 314³.
If a cube with a side length of 414 cm is compared to a cube with a side length of 14 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 414 cm is 70,878,744 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 414 means multiplying 414 by itself three times: 414 × 414 = 171,396, and then 171,396 × 414 = 70,878,744.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 70,878,744 cm³.
Estimate the cube 413.9 using the cube 414.
The cube of 413.9 is approximately 70,878,744.
First, identify the cube of 414, The cube of 414 is 414³ = 70,878,744.
Since 413.9 is only a tiny bit less than 414, the cube of 413.9 will be almost the same as the cube of 414.
The cube of 413.9 is approximately 70,878,744 because the difference between 413.9 and 414 is very small.
So, we can approximate the value as 70,878,744.
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.