Cube Root of 31
The value of the cube root of 31 rounded to 5 decimal places is 3.14138. It is the real solution of the equation x^{3} = 31. The cube root of 31 is expressed as ∛31 in the radical form and as (31)^{⅓} or (31)^{0.33} in the exponent form. The prime factorization of 31 is 31, hence, the cube root of 31 in its lowest radical form is expressed as ∛31.
 Cube root of 31: 3.141380652
 Cube root of 31 in Exponential Form: (31)^{⅓}
 Cube root of 31 in Radical Form: ∛31
1.  What is the Cube Root of 31? 
2.  How to Calculate the Cube Root of 31? 
3.  Is the Cube Root of 31 Irrational? 
4.  FAQs on Cube Root of 31 
What is the Cube Root of 31?
The cube root of 31 is the number which when multiplied by itself three times gives the product as 31. The number 31 is prime. Therefore, the cube root of 31 = ∛31 = 3.1414.
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How to Calculate the Value of the Cube Root of 31?
Cube Root of 31 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 = 31
Let us assume x as 3
[∵ 3^{3} = 27 and 27 is the nearest perfect cube that is less than 31]
⇒ x = 3
Therefore,
∛31 = 3 (3^{3} + 2 × 31)/(2 × 3^{3} + 31)) = 3.14
⇒ ∛31 ≈ 3.14
Therefore, the cube root of 31 is 3.14 approximately.
Is the Cube Root of 31 Irrational?
Yes, because ∛31 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 31 is an irrational number.
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Cube Root of 31 Solved Examples

Example 1: Given the volume of a cube is 31 in^{3}. Find the length of the side of the cube.
Solution:
Volume of the Cube = 31 in^{3} = a^{3}
⇒ a^{3} = 31
Cube rooting on both sides,
⇒ a = ∛31 in
Since the cube root of 31 is 3.14, therefore, the length of the side of the cube is 3.14 in. 
Example 2: What is the value of ∛31 + ∛(31)?
Solution:
The cube root of 31 is equal to the negative of the cube root of 31.
i.e. ∛31 = ∛31
Therefore, ∛31 + ∛(31) = ∛31  ∛31 = 0

Example 3: The volume of a spherical ball is 31π in^{3}. What is the radius of this ball?
Solution:
Volume of the spherical ball = 31π in^{3}
= 4/3 × π × R^{3}
⇒ R^{3} = 3/4 × 31
⇒ R = ∛(3/4 × 31) = ∛(3/4) × ∛31 = 0.90856 × 3.14138 (∵ ∛(3/4) = 0.90856 and ∛31 = 3.14138)
⇒ R = 2.85413 in^{3}
FAQs on Cube Root of 31
What is the Value of the Cube Root of 31?
The value of the cube root of 31 is 3.14138.
Why is the Value of the Cube Root of 31 Irrational?
The value of the cube root of 31 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛31 is irrational.
How to Simplify the Cube Root of 31/64?
We know that the cube root of 31 is 3.14138 and the cube root of 64 is 4. Therefore, ∛(31/64) = (∛31)/(∛64) = 3.141/4 = 0.7853.
What is the Cube Root of 31?
The cube root of 31 is equal to the negative of the cube root of 31. Therefore, ∛31 = (∛31) = (3.141) = 3.141.
What is the Cube of the Cube Root of 31?
The cube of the cube root of 31 is the number 31 itself i.e. (∛31)^{3} = (31^{1/3})^{3} = 31.
If the Cube Root of 31 is 3.14, Find the Value of ∛0.031.
Let us represent ∛0.031 in p/q form i.e. ∛(31/1000) = 3.14/10 = 0.31. Hence, the value of ∛0.031 = 0.31.