Cube root of 217
2026-02-28 12:57 Diff
https://brightchamps.com/en-us/math/algebra/cube-root-of-217

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Last updated on August 5, 2025

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.

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
 

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.
     

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:
 

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Problem 1

Find ∛217 + ∛117?

Okay, lets begin

∛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.

Okay, lets begin

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.

Okay, lets begin

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?

Yes, 217 is not divisible by 7 as it does not leave any remainder when division is done. 217 ÷ 7 = 31.
 

2.What is the cube of 217?

The cube of 217 is 217 x 217 x 217 = 10218313.
 

3.What is the symbol for the cube root?

The symbol that is used to represent the cube root is ∛, is different from the square root symbol as it has 3 on the top left of the radical symbol.
 

4.What is the prime factorization form of 217?

5.What is the perfect cube number?

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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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

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