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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 x^{3} = 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
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: 2^{3}
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 x^{3} − 8 = 0.
Solution:
x^{3} − 8 = 0 i.e. x^{3} = 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 x^{3} − 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 in^{3}. What is the radius of this ball?
Solution:
Volume of the spherical ball = 8π in^{3}
= 4/3 × π × R^{3}
⇒ R^{3} = 3/4 × 8
⇒ R = ∛(3/4 × 8) = ∛(3/4) × ∛8 = 0.90856 × 2 (∵ ∛(3/4) = 0.90856 and ∛8 = 2)
⇒ R = 1.81712 in^{3}
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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