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

Cube Root of 4

The value of the cube root of 4 rounded to 6 decimal places is 1.587401. It is the real solution of the equation x³ = 4. The cube root of 4 is expressed as ∛4 in the radical form and as (4)^⅓ or (4)^0.33 in the exponent form. The prime factorization of 4 is 2 × 2, hence, the cube root of 4 in its lowest radical form is expressed as ∛4.

Cube root of 4: 1.587401052
Cube root of 4 in Exponential Form: (4)^⅓
Cube root of 4 in Radical Form: ∛4

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

What is the Cube Root of 4?

The cube root of 4 is the number which when multiplied by itself three times gives the product as 4. Since 4 can be expressed as 2 × 2. Therefore, the cube root of 4 = ∛(2 × 2) = 1.5874.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 4?

Cube Root of 4 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 = 4
Let us assume x as 1
[∵ 1³ = 1 and 1 is the nearest perfect cube that is less than 4]
⇒ x = 1
Therefore,
∛4 = 1 (1³ + 2 × 4)/(2 × 1³ + 4)) = 1.5
⇒ ∛4 ≈ 1.5
Therefore, the cube root of 4 is 1.5 approximately.

Is the Cube Root of 4 Irrational?

Yes, because ∛4 = ∛(2 × 2) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 4 is an irrational number.

☛ Also Check:

Cube Root of 4 Solved Examples

Example 1: Given the volume of a cube is 4 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 4 in³ = a³
⇒ a³ = 4
Cube rooting on both sides,
⇒ a = ∛4 in
Since the cube root of 4 is 1.59, therefore, the length of the side of the cube is 1.59 in.
Example 2: The volume of a spherical ball is 4π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 4π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 4
⇒ R = ∛(3/4 × 4) = ∛(3/4) × ∛4 = 0.90856 × 1.5874 (∵ ∛(3/4) = 0.90856 and ∛4 = 1.5874)
⇒ R = 1.44225 in³
Example 3: What is the value of ∛4 + ∛(-4)?

Solution:

The cube root of -4 is equal to the negative of the cube root of 4.
i.e. ∛-4 = -∛4

Therefore, ∛4 + ∛(-4) = ∛4 - ∛4 = 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 4

What is the Value of the Cube Root of 4?

We can express 4 as 2 × 2 i.e. ∛4 = ∛(2 × 2) = 1.5874. Therefore, the value of the cube root of 4 is 1.5874.

What is the Value of 5 Plus 9 Cube Root 4?

The value of ∛4 is 1.587. So, 5 + 9 × ∛4 = 5 + 9 × 1.587 = 19.283. Hence, the value of 5 plus 9 cube root 4 is 19.283.

If the Cube Root of 4 is 1.59, Find the Value of ∛0.004.

Let us represent ∛0.004 in p/q form i.e. ∛(4/1000) = 1.59/10 = 0.16. Hence, the value of ∛0.004 = 0.16.

Why is the Value of the Cube Root of 4 Irrational?

The value of the cube root of 4 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛4 is irrational.

How to Simplify the Cube Root of 4/343?

We know that the cube root of 4 is 1.5874 and the cube root of 343 is 7. Therefore, ∛(4/343) = (∛4)/(∛343) = 1.587/7 = 0.2267.

What is the Cube of the Cube Root of 4?

The cube of the cube root of 4 is the number 4 itself i.e. (∛4)³ = (4^1/3)³ = 4.