Cube Root of 216
2026-02-28 08:26 Diff
https://brightchamps.com/en-us/math/algebra/cube-root-of-216

631 Learners

Last updated on August 5, 2025

The cube root of 216 is the value “y” such that the number “y” is multiplied thrice by itself. ∛ is the symbol used to denote the cube root of a number. Cube roots are used in designing loudspeakers or in pharmacology for correct dosage of medicine as per body weight.

What Is the Cube Root of 216 ?

The cube root of 216 is 6. The cube root of 216 is expressed as ∛216 in radical form, where the “∛"  sign is called the “radical” sign. In exponential form, it is written as (216)⅓
 

Finding the Cube Root of 216

We can find the cube root of 216, mainly through two methods: 

  • Prime Factorization method.
  • Subtraction method 

Cubic Root of 216 By Prime Factorization

Finding a cube root of 216 through the Prime Factorization method involves determining the factor of 216.


Step 1: Find the prime factors of 216. 
So 216 = 2×2×2×3×3×3


Step 2:Group the factors of 216 in a group of 3.


Step 3: Since 216 is a perfect cube, we have two pairs of 3 digits.


The cube root of 216 can be written as ∛216 = ∛(2×2×2)×(3×3×3) = 2×3 = 6 


Therefore, the cube root of 216 is 6. 
 

Explore Our Programs

Cube Root of 216 By Subtraction Method

The subtraction method involves subtracting successive odd numbers repeatedly. 


Subtract the numbers 1,7,19,37,61,91,127,169,217,331,397……..successively till we get a zero. 

Step 1:Subtract the 1st odd number : 216–1 = 215 


Step 2:Subtract the next odd number: 215–7 = 208


Step 3: Subtract the next odd number: 208–19 =  189


Step 4: Subtract the next odd number: 189–37 = 152


Step 5: Subtract the next odd number: 152–61 = 91


Step 6: Subtract the next odd number: 91 – 91 = 0


Here, the subtraction took place six times to reach zero.


Hence, the cube root of 216 is 6. 

216–1 = 215

215-7= 208

208-19=189

189-37=152

152-61=91

91-91=0 

Common Mistakes and How to Avoid Them in Cube Root of 216

While finding the cube root of 216, there are some common mistakes that we often make. So let’s discuss a few of the mistakes and their solutions.
 

Download Worksheets

Problem 1

Given the volume of a cube is 216 cubic inches, find the length of one side of the cube.

Okay, lets begin

6 inches.
 

Explanation

 Volume of cube = a3, where a is the side length

Equation:  a3= 216 

Apply the cube root:  a = ∛216

Simplify:

a = ∛2×2×2×3×3×3

= 2×3

= 6
 

Well explained 👍

Problem 2

Express the cube root of 216 in exponential form.

Okay, lets begin

(216)⅓
 

Explanation

The cube root of any number can be expressed as (a)⅓ 
 

Well explained 👍

Problem 3

Find the cube root of 216 by estimation method.

Okay, lets begin

 6
 

Explanation

 Find nearby perfect cubes: 53 = 125 and 63 = 216, Since 216 is exactly 63, the cube root is 6.
 

Well explained 👍

Conclusion

We get a cube root of a number when multiplied by itself three times. Methods like Prime Factorization, and subtraction methods are useful in finding the cube root of a perfect cube. Since we have found the cube root of 216 using both these methods, it has become quite simple to find the cube roots of any other number. 
 

FAQs on 216 cube root

1.How to solve the ∛225 ?

By prime factorization method:

 225 = ∛3×3×5×5

= 6.0822
 

2.Is 0 a cube number ?

3.Is 27 a multiple of 9 ?

4.Is Pi (π) a real number ?

5.Can the cube root of 216 be negative?

The cube root of 216 is 6 but if we consider the cube root of a negative number then the cube root would be negative. 
 

6.What is the relationship between the cube root of 216 and the square root of 216 ?

 There is no relationship between the cube root of 216 and the square root of 216.
 

Important Glossaries for Cube Root of 216

  • Exponent : It is the number that indicates how many times a base is multiplied by itself
  • Radicand: It is the number that indicates how many times a base is multiplied by itself. 
  • Radical symbol: It is the symbol used to denote roots of numbers.
  • Volume of cube: It is the amount of space occupied by a cube. 
     

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.