Cube Root of 1
The value of the cube root of 1 is 1 itself. It is the real solution of the equation x^{3} = 1. The cube root of 1 is expressed as ∛1 in radical form and as (1)^{⅓} or (1)^{0.33} in the exponent form. As the cube root of 1 is a whole number, 1 is a perfect cube.
 Cube root of 1: 1
 Cube root of 1 in exponential form: (1)^{⅓}
 Cube root of 1 in radical form: ∛1
1.  What is the Cube Root of 1? 
2.  How to Calculate the Cube Root of 1? 
3.  Is the Cube Root of 1 Irrational? 
4.  FAQs on Cube Root of 1 
What is the Cube Root of 1?
The cube root of 1 is the number which when multiplied by itself three times gives the product as 1. In fact, the nth root of 1 is always 1. Therefore, the cube root of 1 = ∛1 = 1.
Is the Cube Root of 1 Irrational?
No, because ∛1 can be expressed in the form of p/q i.e. 1/1. Therefore, the value of the cube root of 1 is rational.
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Cube Root of 1 Solved Examples

Example 1: The volume of a spherical ball is π in^{3}. What is the radius of this ball?
Solution:
Volume of the spherical ball = π in^{3}
= 4/3 × π × R^{3}
⇒ R^{3} = 3/4
⇒ R = ∛(3/4 × 1) = ∛(3/4) = 0.90856 (∵ ∛(3/4) = 0.90856)
⇒ R = 0.90856 in^{3} 
Example 2: Given the volume of a cube is 1 in^{3}. Find the length of the side of the cube.
Solution:
Volume of the Cube = 1 in^{3} = a^{3}
⇒ a^{3} = 1
Cube rooting on both sides,
⇒ a = ∛1 in
Therefore, the length of the side of the cube is 1 in. 
Example 3: Find the real root of the equation x^{3} − 1 = 0.
Solution:
x^{3} − 1 = 0 i.e. x^{3} = 1
Solving for x gives us,
x = ∛1, x = ∛1 × (1 + √3i))/2 and x = ∛1 × (1  √3i))/2
where i is called the imaginary unit and is equal to √1.
Ignoring imaginary roots,
x = ∛1 = 1
Therefore, the real root of the equation x^{3} − 1 = 0 is for x = 1.
FAQs on Cube Root of 1
What is the Value of the Cube Root of 1?
The value of the cube root of 1 is 1 itself.
What is the Square of the Cube Root of 1?
The square of the cube root of 1 is the number 1 itself i.e. (∛1)^{2} = (1)^{2} = 1.
Why is the value of the Cube Root of 1 Rational?
The value of the cube root of 1 can be expressed in the form of p/q i.e. = 1/1, where q ≠ 0. Therefore, the ∛1 is rational.
What is the Value of ∛0.001?
Let us represent ∛0.001 in p/q form i.e. ∛(1/1000) = 1/10 = 0.1. Hence, the value of ∛0.001 = 0.1.
How to Simplify the Cube Root of 1/27?
We know that the cube root of 1 is 1 and the cube root of 27 is 3. Therefore, ∛(1/27) = (∛1)/(∛27) = 1/3 = 0.3333.
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