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109 Learners

Last updated on ** September 26th, 2024**

The cube root of 216 is the value āyā such that the number āyā is multiplied thrice by itself. ā 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 ā216 in radical form, where the “ā" sign is called the “radical” sign. In exponential form, it is written as (216)^{ā
}

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 ā216 = ā(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.