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Cube Root of 1

The value of the cube root of 1 is 1 itself. It is the real solution of the equation x³ = 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

Cube Root of 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 n-th 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 in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = π in³
= 4/3 × π × R³
⇒ R³ = 3/4
⇒ R = ∛(3/4 × 1) = ∛(3/4) = 0.90856 (∵ ∛(3/4) = 0.90856)
⇒ R = 0.90856 in³
Example 2: Given the volume of a cube is 1 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 1 in³ = a³
⇒ a³ = 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 x³ − 1 = 0.

Solution:

x³ − 1 = 0 i.e. x³ = 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 x³ − 1 = 0 is for x = 1.

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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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