Last updated on May 26th, 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.
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
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.
Given the volume of a cube is 216 cubic inches, find the length of one side of the cube.
6 inches.
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
Express the cube root of 216 in exponential form.
(216)⅓
The cube root of any number can be expressed as (a)⅓
Find the cube root of 216 by estimation method.
6
Find nearby perfect cubes: 53 = 125 and 63 = 216, Since 216 is exactly 63, the cube root is 6.
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.
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.
: He loves to play the quiz with kids through algebra to make kids love it.