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Last updated on November 30th, 2024

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Cube Root of 216

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Foundation
Intermediate
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The cube root of 216 is the value ā€œyā€ such that the number ā€œyā€ is multiplied thrice by itself. āˆ› 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 āˆ›216 in radical form, where the “āˆ›"  sign is called the “radical” sign. In exponential form, it is written as (216)ā…“
 

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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 āˆ›216 = āˆ›(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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