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Cube Root of 8

The value of the cube root of 8 is 2. It is the real solution of the equation x³ = 8. The cube root of 8 is expressed as ∛8 in radical form and as (8)^⅓ or (8)^0.33 in the exponent form. As the cube root of 8 is a whole number, 8 is a perfect cube.

Cube root of 8: 2
Cube root of 8 in exponential form: (8)^⅓
Cube root of 8 in radical form: ∛8

Cube Root of 8

1.	What is the Cube Root of 8?
2.	How to Calculate the Cube Root of 8?
3.	Is the Cube Root of 8 Irrational?
4.	FAQs on Cube Root of 8

What is the Cube Root of 8?

The cube root of 8 is the number which when multiplied by itself three times gives the product as 8. Since 8 can be expressed as 2 × 2 × 2. Therefore, the cube root of 8 = ∛(2 × 2 × 2) = 2.

How to Calculate the Value of the Cube Root of 8?

Cube Root of 8 by Prime Factorization

Prime factorization of 8 is 2 × 2 × 2
Simplifying the above expression: 2³

Therefore, the cube root of 8 by prime factorization is (2 × 2 × 2)^1/3 = 2.

Is the Cube Root of 8 Irrational?

No, because ∛8 = ∛(2 × 2 × 2) can be expressed in the form of p/q i.e. 2/1. Therefore, the value of the cube root of 8 is an integer (rational).

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Cube Root of 8 Solved Examples

Example 1: Find the real root of the equation x³ − 8 = 0.

Solution:

x³ − 8 = 0 i.e. x³ = 8
Solving for x gives us,
x = ∛8, x = ∛8 × (-1 + √3i))/2 and x = ∛8 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛8
Therefore, the real root of the equation x³ − 8 = 0 is for x = ∛8 = 2.
Example 2: What is the value of ∛8 + ∛(-8)?

Solution:

The cube root of -8 is equal to the negative of the cube root of 8.
i.e. ∛-8 = -∛8

Therefore, ∛8 + ∛(-8) = ∛8 - ∛8 = 0
Example 3: The volume of a spherical ball is 8π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 8π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 8
⇒ R = ∛(3/4 × 8) = ∛(3/4) × ∛8 = 0.90856 × 2 (∵ ∛(3/4) = 0.90856 and ∛8 = 2)
⇒ R = 1.81712 in³

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FAQs on Cube Root of 8

What is the Value of the Cube Root of 8?

We can express 8 as 2 × 2 × 2 i.e. ∛8 = ∛(2 × 2 × 2) = 2. Therefore, the value of the cube root of 8 is 2.

What is the Cube Root of -8?

The cube root of -8 is equal to the negative of the cube root of 8. Therefore, ∛-8 = -(∛8) = -(2) = -2.

Is 8 a Perfect Cube?

The number 8 on prime factorization gives 2 × 2 × 2. On combining the prime factors in groups of 3 gives 2. So, the cube root of 8 = ∛(2 × 2 × 2) = 2 (perfect cube).

How to Simplify the Cube Root of 8/512?

We know that the cube root of 8 is 2 and the cube root of 512 is 8. Therefore, ∛(8/512) = (∛8)/(∛512) = 2/8 = 0.25.

If the Cube Root of 8 is 2, Find the Value of ∛0.008.

Let us represent ∛0.008 in p/q form i.e. ∛(8/1000) = 2/10 = 0.2. Hence, the value of ∛0.008 = 0.2.

Why is the value of the Cube Root of 8 Rational?

The value of the cube root of 8 can be expressed in the form of p/q i.e. = 2/1, where q ≠ 0. Therefore, the ∛8 is rational.

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