from a handpicked tutor in LIVE 1to1 classes
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 x^{3} = 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 ((x^{3} + 2a)/(2x^{3} + 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
[∵ 1^{3} = 1 and 1 is the nearest perfect cube that is less than 4]
⇒ x = 1
Therefore,
∛4 = 1 (1^{3} + 2 × 4)/(2 × 1^{3} + 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 1
 Cube Root of 384
 Cube Root of 2304
 Cube Root of 108
 Cube Root of 41
 Cube Root of 288
 Cube Root of 320
Cube Root of 4 Solved Examples

Example 1: Given the volume of a cube is 4 in^{3}. Find the length of the side of the cube.
Solution:
Volume of the Cube = 4 in^{3} = a^{3}
⇒ a^{3} = 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 in^{3}. What is the radius of this ball?
Solution:
Volume of the spherical ball = 4π in^{3}
= 4/3 × π × R^{3}
⇒ R^{3} = 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 in^{3} 
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
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.
visual curriculum