cube root of 216

Cube Root of 216 is 6

We define cube root as the number which when multiplied by itself twice results in the original number. The radical form of the cube root of 216 is ∛216, while the exponent form is (216)^1/3.

Cube Root of 216

• Cube Root of 216: 2
• Cube Root of 216 in Exponential Form: (216)^⅓
• Cube Root of 216 in Radical Form: ∛(216)

This article will teach us how to calculate the cube root of 216 using a variety of techniques and provide several examples with solutions.

What is Cube Root of 216?

Cube Root of 216 is a value that when multiplied by itself three times results in 512. Now we all know that 216 = 6 × 6 × 6, so it is clear that multiplying 6 three times results in 216 thus, the cube root of 216 is 6.

Mathematically, if x is the cube root of 216, it can be represented as:

x³ = 216

⇒ x = (216)^1/3

⇒ x = 6

i.e. cube root of 216 is written as,

∛(216) = 6

Cube Root Definition

A value that returns the original number after being multiplied twice by itself is known as the cube root of a number. Cube root is represented as ∛(x) symbol.

Cube Root of 216 Calculator

How to Find Cube Root of 216?

To find the cube root of 216 various methods can be used that are given below:

• Cube Root of 216 by Successive Subtraction Method
• Cube Root of 216 by Prime Factorization Method

Now let’s find the cube root of 216 using the above-mentioned methods.

Cube Root of 216 by Successive Subtraction Method

Let’s find the cube root of 216 by using successive subtraction methods; So, Here we start with 1, subtracting each odd number until the outcome is less than the subsequent odd number.

• 216 – 1 = 215
• 215 – 3 = 212
• 212 – 5 = 207
• 207 – 7 = 200
• 200 – 9 = 191
• 191 – 11 = 180

180 is the outcome, and 13 is the next odd integer that will give;

• 180 – 13 = 167

Amount of times we subtracted (6) plus 1 is the cube root, which is 6 + 1 = 7.

Therefore, the cube root of 216 by successive subtraction method is 6.

Cube Root of 216 by Prime Factorization Method

Prime factorization of 216 is found by dividing it repeatedly by prime numbers, starting at 2, until we are unable to divide it any further:

⇒ 216 = 2 × 2 × 2 × 3 × 3 × 3

Prime Factors of 216

⇒ 216 = 2³ × 3³

⇒ ∛(216) = 2 × 3 = 6

Therefore, the cube root of 216 is 6 is resolved by the prime factorization method.

Is Cube Root of 216 a Rational or Irrational Number?

If any number is expressed in the form of p/q, where q is not equal to 0, then the number is called a rational number. Here we see that the cube root of 216 is 6, i.e. represented as, 6/1 a rational number. So

(216)^1/3 = 6

Cube Root of 216 Solved Examples

Example 1: Simplify ∛(216) – ∛(-216).

Solution:

We know,

∛(216) = 6

∛(-216) = -6

Hence, ∛(216) – ∛(-216) = 6 – (-6) = 6 + 6 = 12

Example 2: Simplify ∛(216) × ∛(-216)

Solution:

We know,

∛(216) = 6

∛(-216) = -6

Hence, ∛(216) × ∛(-216) = 6 × (-6) = -36

Example 3: Simplify ∛(216) + ∛(-216)

Solution:

We know,

∛(216) = 6

∛(-216) = -6

Hence, ∛(216) + ∛(-216) = 6 + (-6) = 6 – 6 = 0

Cube Root of 216-FAQs

What is Value of Cube Root of 216?

Cube root of 216 is 6.

Is cube root of 216 a rational number?

Yes, cube root of 216 is a rational number because it can be expressed in the form of two integers.

What is cube root of 216 in radical form?

Cube root of 216 can be expressed as ∛ (216) in radical form.

What methods are used to find cube root of 216?

For finding the cube root of 216, we use

• Successive Subtraction Method
• Prime Factorization Method

What is cube root of negative 216?

Cube root of (-216) is (-6).

Is 216 a Perfect Cube?

Cube root of 216 is 6, which is a whole number, therefore, 216 is a perfect cube.