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Last updated on November 30th, 2024
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.
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:
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.