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Last updated on May 26th, 2025

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Cube root of 217

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The cube root of a number is a value that when multiplied thrice by itself results back to the original number. Imagine you have a cube (box) with a known volume. The cube root would then be useful to determine the length of one side of the box.

Cube root of 217 for UAE Students
Professor Greenline from BrightChamps

What is the cube root of 217?

The cube root of 217 is a number , when you multiply it by itself three times, it gives 217. Let’s check a few steps and methods to calculate the cube root of 700.


Cube root of 217: ∛217 = 6.006


Exponential form of the cube root of 217 is 2171/3


Radical form of the cube root of 217 is ∛217
 

Professor Greenline from BrightChamps

Finding the Cube Root of 217

Use the following methods to find the cube root of a number:

 

 

  • Prime factorization
  • Approximation method
  • Long division 
  • Subtraction method
  • Halley’s method — is used when a number is not a perfect cube.
     
Professor Greenline from BrightChamps

Cube root of 217 using the Halley’s Method

We use the below formula to find the cube root using Halley’s Method:


∛a≅ x((x3+2a) / (2x3+a))


In the formula,
a = given number, 217
x = an approximate number close to the cube root of the number, 217. Let’s say x is 6. Therefore, 63 = 216.


Now, let’s apply the formula and find the cube root.


Here, a = 217 and x = 6


Now apply the formula: 


∛a≅ x((x3+2a) / (2x3+a))


∛217 ≅ 6((63+2 × 217) / (2 × 63+217)) 

 

∛217 ≅ 6(( 216+434 ) / (2 x 216 + 217))


∛217 ≅ 6((650) / (649))


∛217 ≅   6(1.001)


∛217 ≅  6.006
 

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Common Mistakes and How to Avoid Them in the Cube Root of 217

While learning  cube roots,it’s common for students to make mistakes, to avoid those here are some common mistakes listed below:
 

Mistake 1

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Getting Confused With the Cube Root and Square Root

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 Students sometimes multiply the same number twice instead of three times, which makes it a square root and not a cube root. This results in improper results to avoid this student needing to have  a clear idea about roots.
 

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Cube Root of 217 Examples

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Max, the Girl Character from BrightChamps

Problem 1

Find ∛217 + ∛117?

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∛217 + ∛117


= 6.006 + 4.890 


= 10.896.
 

Explanation

To find the solution for ∛217 + ∛117, the value of ∛217 and ∛117 must be found and then added together. The answer is 10.899.
 

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Problem 2

Solve for x if x³ = 217.

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x3 = 217


Value of x = ∛217


x = 6.006.

Explanation

To find the value of x, the given value of x3 is to be inverse and the cube root of 217 is to be found. Therefore, the answer will be 6.009.
 

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Max, the Girl Character from BrightChamps

Problem 3

The side length ‘s’ of a square is ∛217, find the area of the area of the square.

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Length of a square ‘s’ = ∛217


The equation to find the area of square = a2


= ∛217 x ∛217


 = 6.006 × 6.006


 = 36.072.
 

Explanation

 The formula to find the area of a square is a2, which is ∛217 multiplied twice. Thus, the area of the square is 36.072. 
 

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FAQs For “Cube Root Of 217”

1.Is 217 divisible by 7?

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2.What is the cube of 217?

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3.What is the symbol for the cube root?

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4.What is the prime factorization form of 217?

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5.What is the perfect cube number?

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6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?

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7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Cube root of 217?

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8.How do technology and digital tools in United Arab Emirates support learning Algebra and Cube root of 217?

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9.Does learning Algebra support future career opportunities for students in United Arab Emirates?

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Professor Greenline from BrightChamps

Important Glossaries for Cube Root of 217

  • Whole numbers — The whole numbers are the set of numbers that includes all the positive integers and zero. Example: 0,1,2,3………

 

  • Square root  —A number’s square root is considered as a number that when it is multiplied by itself gives us the original number.Example: √4 is 2.

 

  • Exponent: It is a number which shows how many times a base number should be multiplied by itself.Example: 42=  4 x 4 = 16

 

  • Irrational number: The number that cannot be written in the form of a fraction.Example: √2 is an irrational number.
Professor Greenline from BrightChamps

About BrightChamps in United Arab Emirates

At BrightChamps, we recognize algebra as more than numbers—it’s the pathway to endless possibilities! We strive to help children across the UAE master key math skills, focusing today on the Cube root of 217 with an emphasis on understanding cube roots—in a lively, enjoyable, and easy-to-understand way. Whether your child is figuring out the speed of a roller coaster at Dubai Parks and Resorts, keeping track of scores at a local football match, or managing their allowance to buy the latest gadgets, mastering algebra builds confidence for daily challenges. Our interactive lessons are designed to be fun and simple. Aware that children in the UAE learn in various ways, we personalize our teaching to each child’s style. From the towering skyscrapers of Dubai to the cultural heritage of Abu Dhabi, BrightChamps brings math to life, making it engaging throughout the UAE. Let’s make cube roots an enjoyable part of every child’s math journey!
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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.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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