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Cube root of 216- value and calculation

On multiplying a number three times by itself, the resultant number is the cube of that number. The cube root is the inverse function of the cube i.e, the number which is multiplied thrice is the cube root of the resultant number. The symbol of the cube root is denoted by ∛. So, In this article, we will discuss the cube root of 216 and the prime factorisation method to find its cube root.

 

CUBE ROOT OF 216

The cube root of 216 is equal to 6. This means that when we multiply the number 6 three times by itself, we get the product 216.

How to find the cube root?

To find the cube root of a number, we can use the prime factorisation method. By evaluating the prime factors we will make the groups of threes of the same digits and the cube is eliminated by the cube root. This is the easiest method to find the cube root of any number.

How to calculate the cube root of 216?

On performing the prime factorisation of 216, we get- 2×3×2×3×2×3.

The groups of threes of the same factors = 23×33

On applying the cube root, we get ∛(2×3)3 =  ∛63, which is equal to 6.

Hence, 6 is the cube root of 216.

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Frequently Asked Questions

Q1. How many real cube roots does 216 have?

Ans. Every real number has only one cube root so 216 is a real number, it has only one cube root which is 6.

 

Q2. Is the cube root of 216 irrational?

Ans. The cube root of 216 is 6, which is a rational number as it can be written in the form of

and q≠0. Therefore, the cube root of 216 is not an irrational number.

 

Q3. When 216 is divided by 27, we get the cube of which number.

Sol. The prime factors of 216 = 23×33

= 8×27

When 216 is divided by 27 = 216/27

=  8 = 2×2×2

= 23

Hence, when 216 is divided by 27, we will get the cube of 2 i.e, 8.