101 LearnersLast updated on June 3rd, 2025
Cube of 217
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.
Cube 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.
How to Calculate the Value of Cube of 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.
- By Multiplication Method
- Using a Formula
- Using a Calculator
By Multiplication Method
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.
Using a Formula (a³)
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.
Using a Calculator
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.
Tips and Tricks for the Cube of 217
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.
Common Mistakes to Avoid When Calculating the Cube of 217
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:
Mistake 1
Incorrect Multiplication
Kids might multiply the numbers only twice. That is, 217 × 217 and not 217 × 217 × 217. Always remember that 217³ = 217 × 217 × 217.
Solved Examples on Cube of 217
Problem 1
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.
Explanation
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.
Problem 2
If the side length of the cube is 217 cm, what is the volume?
The volume is 10,217,913 cm³.
Explanation
Use the volume formula for a cube V = Side³.
Substitute 217 for the side length: V = 217³ = 10,217,913 cm³.
Problem 3
How much larger is 217³ than 207³?
217³ – 207³ = 3,344,000.
Explanation
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.
Problem 4
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.
Explanation
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.
Problem 5
Estimate the cube of 216.9 using the cube of 217.
The cube of 216.9 is approximately 10,217,913.
Explanation
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.
FAQs on Cube of 217
1.What are the perfect cubes up to 217?
2.How do you calculate 217³?
3.What is the meaning of 217³?
4.What is the cube root of 217?
5.Is 217 a perfect cube?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Cube of 217?
8.How do technology and digital tools in Vietnam support learning Algebra and Cube of 217?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for Cube of 217
- Binomial Formula: It is an algebraic expression used to expand the powers of a number, written as (a + b)ⁿ, where ‘n’ is a positive integer raised to the base. The formula is used to find the square and cube of a number.
- Cube of a Number: Multiplying a number by itself three times is called the cube of a number.
- Exponential Form: It is a way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, 2³ represents 2 × 2 × 2, which equals 8.
- Perfect Cube: A perfect cube is an integer that is the cube of another integer.
- Volume of a Cube: The volume of a cube is calculated as the side length raised to the power of three (side³).
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Jaskaran Singh Saluja
About the Author
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.
Fun Fact
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