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
 

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

• Prime Factorization method.

• Subtraction method 

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. 
 

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 

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. 
 

• 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.