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Last updated on November 30th, 2024

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Cube Root of 216

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Foundation
Intermediate
Advance Topics

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.

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What Is the Cubic 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)
 

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Finding the Cubic Root of 216

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

 

  • Prime Factorization method.

 

  • Subtraction method 
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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
 

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Cubic 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 


 

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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. 
 

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Important Glossaries for Cubic 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. 
     
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