Cube Root of 5
The value of the cube root of 5 rounded to 6 decimal places is 1.709976. It is the real solution of the equation x^{3} = 5. The cube root of 5 is expressed as ∛5 in the radical form and as (5)^{⅓} or (5)^{0.33} in the exponent form. The prime factorization of 5 is 5, hence, the cube root of 5 in its lowest radical form is expressed as ∛5.
 Cube root of 5: 1.709975947
 Cube root of 5 in Exponential Form: (5)^{⅓}
 Cube root of 5 in Radical Form: ∛5
1.  What is the Cube Root of 5? 
2.  How to Calculate the Cube Root of 5? 
3.  Is the Cube Root of 5 Irrational? 
4.  FAQs on Cube Root of 5 
What is the Cube Root of 5?
The cube root of 5 is the number which when multiplied by itself three times gives the product as 5. The number 5 is prime. Therefore, the cube root of 5 = ∛5 = 1.71.
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How to Calculate the Value of the Cube Root of 5?
Cube Root of 5 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 = 5
Let us assume x as 1
[∵ 1^{3} = 1 and 1 is the nearest perfect cube that is less than 5]
⇒ x = 1
Therefore,
∛5 = 1 (1^{3} + 2 × 5)/(2 × 1^{3} + 5)) = 1.57
⇒ ∛5 ≈ 1.57
Therefore, the cube root of 5 is 1.57 approximately.
Is the Cube Root of 5 Irrational?
Yes, because ∛5 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 5 is an irrational number.
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Cube Root of 5 Solved Examples

Example 1: Find the real root of the equation x^{3} − 5 = 0.
Solution:
x^{3} − 5 = 0 i.e. x^{3} = 5
Solving for x gives us,
x = ∛5, x = ∛5 × (1 + √3i))/2 and x = ∛5 × (1  √3i))/2
where i is called the imaginary unit and is equal to √1.
Ignoring imaginary roots,
x = ∛5
Therefore, the real root of the equation x^{3} − 5 = 0 is for x = ∛5 = 1.71.

Example 2: Given the volume of a cube is 5 in^{3}. Find the length of the side of the cube.
Solution:
Volume of the Cube = 5 in^{3} = a^{3}
⇒ a^{3} = 5
Cube rooting on both sides,
⇒ a = ∛5 in
Since the cube root of 5 is 1.71, therefore, the length of the side of the cube is 1.71 in. 
Example 3: What is the value of ∛5 ÷ ∛(5)?
Solution:
The cube root of 5 is equal to the negative of the cube root of 5.
⇒ ∛5 = ∛5
Therefore,
⇒ ∛5/∛(5) = ∛5/(∛5) = 1
FAQs on Cube Root of 5
What is the Value of the Cube Root of 5?
The value of the cube root of 5 is 1.70998.
Why is the Value of the Cube Root of 5 Irrational?
The value of the cube root of 5 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛5 is irrational.
What is the Cube of the Cube Root of 5?
The cube of the cube root of 5 is the number 5 itself i.e. (∛5)^{3} = (5^{1/3})^{3} = 5.
Is 5 a Perfect Cube?
The number 5 is prime. Here, the prime factor 5 is not in the power of 3 and this implies that the cube root of 5 is irrational, hence 5 is not a perfect cube.
What is the Cube Root of 5?
The cube root of 5 is equal to the negative of the cube root of 5. Therefore, ∛5 = (∛5) = (1.71) = 1.71.
What is the Value of 1 Plus 7 Cube Root 5?
The value of ∛5 is 1.71. So, 1 + 7 × ∛5 = 1 + 7 × 1.71 = 12.969999999999999. Hence, the value of 1 plus 7 cube root 5 is 12.969999999999999.