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Cube Root of 216

The value of the cube root of 216 is 6. It is the real solution of the equation x3 = 216. The cube root of 216 is expressed as ∛216 in radical form and as (216)⅓ or (216)0.33 in the exponent form. As the cube root of 216 is a whole number, 216 is a perfect cube.

  • Cube root of 216: 6
  • Cube root of 216 in exponential form: (216)⅓
  • Cube root of 216 in radical form: ∛216

Cube Root of 216

1. What is the Cube Root of 216?
2. How to Calculate the Cube Root of 216?
3. Is the Cube Root of 216 Irrational?
4. FAQs on Cube Root of 216

What is the Cube Root of 216?

The cube root of 216 is the number which when multiplied by itself three times gives the product as 216. Since 216 can be expressed as 2 × 2 × 2 × 3 × 3 × 3. Therefore, the cube root of 216 = ∛(2 × 2 × 2 × 3 × 3 × 3) = 6.

How to Calculate the Value of the Cube Root of 216?

Cube Root of 216 by Prime Factorization

  • Prime factorization of 216 is 2 × 2 × 2 × 3 × 3 × 3
  • Simplifying the above expression: 23 × 33
  • Simplifying further: 63

Therefore, the cube root of 216 by prime factorization is (2 × 2 × 2 × 3 × 3 × 3)1/3 = 6.

Is the Cube Root of 216 Irrational?

No, because ∛216 = ∛(2 × 2 × 2 × 3 × 3 × 3) can be expressed in the form of p/q i.e. 6/1. Therefore, the value of the cube root of 216 is an integer (rational).

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Cube Root of 216 Solved Examples

  1. Example 1: Find the real root of the equation x3 − 216 = 0.

    Solution:

    x3 − 216 = 0 i.e. x3 = 216
    Solving for x gives us,
    x = ∛216, x = ∛216 × (-1 + √3i))/2 and x = ∛216 × (-1 - √3i))/2
    where i is called the imaginary unit and is equal to √-1.
    Ignoring imaginary roots,
    x = ∛216
    Therefore, the real root of the equation x3 − 216 = 0 is for x = ∛216 = 6.

  2. Example 2: Given the volume of a cube is 216 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 216 in3 = a3
    ⇒ a3 = 216
    Cube rooting on both sides,
    ⇒ a = ∛216 in
    Since the cube root of 216 is 6, therefore, the length of the side of the cube is 6 in.

  3. Example 3: What is the value of ∛216 + ∛(-216)?

    Solution:

    The cube root of -216 is equal to the negative of the cube root of 216.
    i.e. ∛-216 = -∛216

    Therefore, ∛216 + ∛(-216) = ∛216 - ∛216 = 0

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FAQs on Cube Root of 216

What is the Value of the Cube Root of 216?

We can express 216 as 2 × 2 × 2 × 3 × 3 × 3 i.e. ∛216 = ∛(2 × 2 × 2 × 3 × 3 × 3) = 6. Therefore, the value of the cube root of 216 is 6.

How to Simplify the Cube Root of 216/343?

We know that the cube root of 216 is 6 and the cube root of 343 is 7. Therefore, ∛(216/343) = (∛216)/(∛343) = 6/7 = 0.8571.

What is the Cube of the Cube Root of 216?

The cube of the cube root of 216 is the number 216 itself i.e. (∛216)3 = (2161/3)3 = 216.

What is the Cube Root of -216?

The cube root of -216 is equal to the negative of the cube root of 216. Therefore, ∛-216 = -(∛216) = -(6) = -6.

Why is the value of the Cube Root of 216 Rational?

The value of the cube root of 216 can be expressed in the form of p/q i.e. = 6/1, where q ≠ 0. Therefore, the ∛216 is rational.

What is the Value of 15 Plus 12 Cube Root 216?

The value of ∛216 is 6. So, 15 + 12 × ∛216 = 15 + 12 × 6 = 87. Hence, the value of 15 plus 12 cube root 216 is 87.

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