Last updated on June 3rd, 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 214.
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 214 can be written as 214³, which is the exponential form. Or it can also be written in arithmetic form as, 214 × 214 × 214.
In order 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 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.
214³ = 214 × 214 × 214
Step 2: Calculate the result.
Hence, the cube of 214 is 9,812,344.
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 214 into two parts, as 200 and 14. Let a = 200 and b = 14, so a + b = 214
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³= 200³ , 3a²b = 3 × 200² × 14 , 3ab² = 3 × 200 × 14² , b³ = 14³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³
(200 + 14)³ = 200³ + 3 × 200² × 14 + 3 × 200 × 14² + 14³ 214³
= 8,000,000 + 1,680,000 + 117,600 + 2,744 214³ = 9,812,344
Step 5: Hence, the cube of 214 is 9,812,344.
To find the cube of 214 using a calculator, input the number 214 and use the cube function (if available) or multiply 214 × 214 × 214. This operation calculates the value of 214³, resulting in 9,812,344. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 2 followed by 1 and 4
Step 3: If the calculator has a cube function, press it to calculate 214³.
Step 4: If there is no cube function on the calculator, simply multiply 214 three times manually.
Step 5: The calculator will display 9,812,344.
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 214?
The cube of 214 is 9,812,344 and the cube root of 214 is approximately 6.012.
First, let’s find the cube of 214. 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 214³ = 9,812,344
Next, we must find the cube root of 214
We know that the cube root of a number ‘x’, such that √³x = y
Where ‘x’ is the given number, and y is the cube root value of the number
So, we get √³214 = 6.012
Hence the cube of 214 is 9,812,344 and the cube root of 214 is approximately 6.012.
If the side length of the cube is 214 cm, what is the volume?
The volume is 9,812,344 cm³.
Use the volume formula for a cube V = Side³.
Substitute 214 for the side length: V = 214³ = 9,812,344 cm³.
How much larger is 214³ than 200³?
214³ – 200³ = 1,812,344.
First, find the cube of 214³, that is 9,812,344
Next, find the cube of 200³, which is 8,000,000
Now, find the difference between them using the subtraction method.
9,812,344 – 8,000,000 = 1,812,344
Therefore, 214³ is 1,812,344 larger than 200³.
If a cube with a side length of 214 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 214 cm is 9,812,344 cm³
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 214 means multiplying 214 by itself three times: 214 × 214 = 45,796, and then 45,796 × 214 = 9,812,344.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 9,812,344 cm³.
Estimate the cube of 213.9 using the cube of 214.
The cube of 213.9 is approximately 9,812,344.
First, identify the cube of 214, The cube of 214 is 214³ = 9,812,344.
Since 213.9 is only a tiny bit less than 214, the cube of 213.9 will be almost the same as the cube of 214.
The cube of 213.9 is approximately 9,812,344 because the difference between 213.9 and 214 is very small.
So, we can approximate the value as 9,812,344.
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.