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 cubes of 217.
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 217 can be written as 217³, which is the exponential form. Or it can also be written in arithmetic form as, 217 × 217 × 217.
In order to check whether a number is a cube number or not, we can use the following three methods: the 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. 217³ = 217 × 217 × 217
Step 2: You get 10,217,913 as the answer.
Hence, the cube of 217 is 10,217,913.
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 217 into two parts. Let a = 200 and b = 17, so a + b = 217.
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³.
Step 3: Calculate each term: a³ = 200³ , 3a²b = 3 × 200² × 17 , 3ab² = 3 × 200 × 17² , b³ = 17³
Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³
(200 + 17)³ = 200³ + 3 × 200² × 17 + 3 × 200 × 17² + 17³ 217³
= 8,000,000 + 2,040,000 + 173,400 + 4,913 217³ = 10,217,913
Step 5: Hence, the cube of 217 is 10,217,913.
To find the cube of 217 using a calculator, input the number 217 and use the cube function (if available) or multiply 217 × 217 × 217. This operation calculates the value of 217³, resulting in 10,217,913. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Enter 217.
Step 3: If the calculator has a cube function, press it to calculate 217³.
Step 4: If there is no cube function on the calculator, simply multiply 217 three times manually.
Step 5: The calculator will display 10,217,913.
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 217?
The cube of 217 is 10,217,913 and the cube root of 217 is approximately 6.002.
First, let’s find the cube of 217. We know that the cube of a number x is such that x³ = y, where x is the given number and y is the cubed value of that number.
So, we get 217³ = 10,217,913.
Next, we must find the cube root of 217.
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 ∛217 ≈ 6.002.
Hence, the cube of 217 is 10,217,913 and the cube root of 217 is approximately 6.002.
If the side length of the cube is 217 cm, what is the volume?
The volume is 10,217,913 cm³.
Use the volume formula for a cube V = Side³.
Substitute 217 for the side length: V = 217³ = 10,217,913 cm³.
How much larger is 217³ than 207³?
217³ – 207³ = 3,344,000.
First, find the cube of 217³, which is 10,217,913.
Next, find the cube of 207³, which is 6,873,913.
Now, find the difference between them using the subtraction method.
10,217,913 – 6,873,913 = 3,344,000
Therefore, 217³ is 3,344,000 larger than 207³.
If a cube with a side length of 217 cm is compared to a cube with a side length of 17 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 217 cm is 10,217,913 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 217 means multiplying 217 by itself three times: 217 × 217 = 47,089, and then 47,089 × 217 = 10,217,913.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 10,217,913 cm³.
Estimate the cube of 216.9 using the cube of 217.
The cube of 216.9 is approximately 10,217,913.
First, identify the cube of 217.
The cube of 217 is 217³ = 10,217,913.
Since 216.9 is only a tiny bit less than 217, the cube of 216.9 will be almost the same as the cube of 217.
The cube of 216.9 is approximately 10,217,913 because the difference between 216.9 and 217 is very small.
So, we can approximate the value as 10,217,913.
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.