A day full of math games & activities. Find one near you.

Cube Root of 3

The value of the cube root of 3 rounded to 6 decimal places is 1.44225. It is the real solution of the equation x³ = 3. The cube root of 3 is expressed as ∛3 in the radical form and as (3)^⅓ or (3)^0.33 in the exponent form. The prime factorization of 3 is 3, hence, the cube root of 3 in its lowest radical form is expressed as ∛3.

Cube root of 3: 1.44224957
Cube root of 3 in Exponential Form: (3)^⅓
Cube root of 3 in Radical Form: ∛3

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

What is the Cube Root of 3?

The cube root of 3 is the number which when multiplied by itself three times gives the product as 3. The number 3 is prime. Therefore, the cube root of 3 = ∛3 = 1.4422.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 3?

Cube Root of 3 by Halley's Method

Its formula is ∛a ≈ x ((x³ + 2a)/(2x³ + a))
where,
a = number whose cube root is being calculated
x = integer guess of its cube root.

Here a = 3
Let us assume x as 1
[∵ 1³ = 1 and 1 is the nearest perfect cube that is less than 3]
⇒ x = 1
Therefore,
∛3 = 1 (1³ + 2 × 3)/(2 × 1³ + 3)) = 1.4
⇒ ∛3 ≈ 1.4
Therefore, the cube root of 3 is 1.4 approximately.

Is the Cube Root of 3 Irrational?

Yes, because ∛3 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 3 is an irrational number.

☛ Also Check:

Cube Root of 3 Solved Examples

Example 1: The volume of a spherical ball is 3π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 3π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 3
⇒ R = ∛(3/4 × 3) = ∛(3/4) × ∛3 = 0.90856 × 1.44225 (∵ ∛(3/4) = 0.90856 and ∛3 = 1.44225)
⇒ R = 1.31037 in³
Example 2: Given the volume of a cube is 3 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 3 in³ = a³
⇒ a³ = 3
Cube rooting on both sides,
⇒ a = ∛3 in
Since the cube root of 3 is 1.44, therefore, the length of the side of the cube is 1.44 in.
Example 3: What is the value of ∛3 + ∛(-3)?

Solution:

The cube root of -3 is equal to the negative of the cube root of 3.
i.e. ∛-3 = -∛3

Therefore, ∛3 + ∛(-3) = ∛3 - ∛3 = 0

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on Cube Root of 3

What is the Value of the Cube Root of 3?

The value of the cube root of 3 is 1.44225.

Why is the Value of the Cube Root of 3 Irrational?

The value of the cube root of 3 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛3 is irrational.

Is 3 a Perfect Cube?

The number 3 is prime. Here, the prime factor 3 is not in the power of 3 and this implies that the cube root of 3 is irrational, hence 3 is not a perfect cube.

What is the Cube Root of -3?

The cube root of -3 is equal to the negative of the cube root of 3. Therefore, ∛-3 = -(∛3) = -(1.442) = -1.442.

What is the Cube of the Cube Root of 3?

The cube of the cube root of 3 is the number 3 itself i.e. (∛3)³ = (3^1/3)³ = 3.

If the Cube Root of 3 is 1.44, Find the Value of ∛0.003.

Let us represent ∛0.003 in p/q form i.e. ∛(3/1000) = 1.44/10 = 0.14. Hence, the value of ∛0.003 = 0.14.