Question

$\sqrt[3]{216}$
Evaluate the term ​

Answer 1

Answer:

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

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

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

Answer 2

Answer:

By prime factoisation, we have

216 = 2×2×2×3×3×3

= (2×2×2)×(3×3×3)

•°•

$\sqrt[ 3]{216} = (2 \times 3) = 6$