Cube Root of 40
The value of the cube root of 40 rounded to 6 decimal places is 3.419952. It is the real solution of the equation x^{3} = 40. The cube root of 40 is expressed as ∛40 or 2 ∛5 in the radical form and as (40)^{⅓} or (40)^{0.33} in the exponent form. The prime factorization of 40 is 2 × 2 × 2 × 5, hence, the cube root of 40 in its lowest radical form is expressed as 2 ∛5.
 Cube root of 40: 3.419951893
 Cube root of 40 in Exponential Form: (40)^{⅓}
 Cube root of 40 in Radical Form: ∛40 or 2 ∛5
1.  What is the Cube Root of 40? 
2.  How to Calculate the Cube Root of 40? 
3.  Is the Cube Root of 40 Irrational? 
4.  FAQs on Cube Root of 40 
What is the Cube Root of 40?
The cube root of 40 is the number which when multiplied by itself three times gives the product as 40. Since 40 can be expressed as 2 × 2 × 2 × 5. Therefore, the cube root of 40 = ∛(2 × 2 × 2 × 5) = 3.42.
☛ Check: Cube Root Calculator
How to Calculate the Value of the Cube Root of 40?
Cube Root of 40 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 = 40
Let us assume x as 3
[∵ 3^{3} = 27 and 27 is the nearest perfect cube that is less than 40]
⇒ x = 3
Therefore,
∛40 = 3 (3^{3} + 2 × 40)/(2 × 3^{3} + 40)) = 3.41
⇒ ∛40 ≈ 3.41
Therefore, the cube root of 40 is 3.41 approximately.
Is the Cube Root of 40 Irrational?
Yes, because ∛40 = ∛(2 × 2 × 2 × 5) = 2 ∛5 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 40 is an irrational number.
☛ Also Check:
 Cube Root of 324
 Cube Root of 121
 Cube Root of 375
 Cube Root of 81
 Cube Root of 72
 Cube Root of 18
 Cube Root of 1024
Cube Root of 40 Solved Examples

Example 1: Find the real root of the equation x^{3} − 40 = 0.
Solution:
x^{3} − 40 = 0 i.e. x^{3} = 40
Solving for x gives us,
x = ∛40, x = ∛40 × (1 + √3i))/2 and x = ∛40 × (1  √3i))/2
where i is called the imaginary unit and is equal to √1.
Ignoring imaginary roots,
x = ∛40
Therefore, the real root of the equation x^{3} − 40 = 0 is for x = ∛40 = 3.42.

Example 2: The volume of a spherical ball is 40π in^{3}. What is the radius of this ball?
Solution:
Volume of the spherical ball = 40π in^{3}
= 4/3 × π × R^{3}
⇒ R^{3} = 3/4 × 40
⇒ R = ∛(3/4 × 40) = ∛(3/4) × ∛40 = 0.90856 × 3.41995 (∵ ∛(3/4) = 0.90856 and ∛40 = 3.41995)
⇒ R = 3.10723 in^{3} 
Example 3: What is the value of ∛40 ÷ ∛(40)?
Solution:
The cube root of 40 is equal to the negative of the cube root of 40.
⇒ ∛40 = ∛40
Therefore,
⇒ ∛40/∛(40) = ∛40/(∛40) = 1
FAQs on Cube Root of 40
What is the Value of the Cube Root of 40?
We can express 40 as 2 × 2 × 2 × 5 i.e. ∛40 = ∛(2 × 2 × 2 × 5) = 3.41995. Therefore, the value of the cube root of 40 is 3.41995.
What is the Cube of the Cube Root of 40?
The cube of the cube root of 40 is the number 40 itself i.e. (∛40)^{3} = (40^{1/3})^{3} = 40.
What is the Cube Root of 40?
The cube root of 40 is equal to the negative of the cube root of 40. Therefore, ∛40 = (∛40) = (3.42) = 3.42.
Why is the Value of the Cube Root of 40 Irrational?
The value of the cube root of 40 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛40 is irrational.
How to Simplify the Cube Root of 40/64?
We know that the cube root of 40 is 3.41995 and the cube root of 64 is 4. Therefore, ∛(40/64) = (∛40)/(∛64) = 3.42/4 = 0.855.
If the Cube Root of 40 is 3.42, Find the Value of ∛0.04.
Let us represent ∛0.04 in p/q form i.e. ∛(40/1000) = 3.42/10 = 0.34. Hence, the value of ∛0.04 = 0.34.