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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 Indian Students
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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
 

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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.
     
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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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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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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 India make better decisions in daily life?

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

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

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9.Does learning Algebra support future career opportunities for students in India?

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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.
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About BrightChamps in India

At BrightChamps, we understand algebra goes beyond symbols—it’s a pathway to limitless opportunities! Our mission is to help children throughout India master vital math skills, with today’s focus on the Cube root of 217 and a special emphasis on grasping cube roots—in a way that’s engaging, enjoyable, and easy to follow. Whether your child is calculating the speed of a passing train, keeping track of scores during a cricket match, or managing pocket money for the latest gadgets, mastering algebra builds the confidence needed for everyday life. Our interactive lessons ensure learning is simple and fun. Aware that children in India learn in various ways, we tailor our teaching to each child’s unique style. From the busy markets of Mumbai to the vibrant streets of Delhi, BrightChamps makes math relatable and exciting all over India. Let’s make cube roots a fun 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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