Cube Root of 52
The value of the cube root of 52 rounded to 7 decimal places is 3.7325112. It is the real solution of the equation x^{3} = 52. The cube root of 52 is expressed as ∛52 in the radical form and as (52)^{⅓} or (52)^{0.33} in the exponent form. The prime factorization of 52 is 2 × 2 × 13, hence, the cube root of 52 in its lowest radical form is expressed as ∛52.
 Cube root of 52: 3.732511157
 Cube root of 52 in Exponential Form: (52)^{⅓}
 Cube root of 52 in Radical Form: ∛52
1.  What is the Cube Root of 52? 
2.  How to Calculate the Cube Root of 52? 
3.  Is the Cube Root of 52 Irrational? 
4.  FAQs on Cube Root of 52 
What is the Cube Root of 52?
The cube root of 52 is the number which when multiplied by itself three times gives the product as 52. Since 52 can be expressed as 2 × 2 × 13. Therefore, the cube root of 52 = ∛(2 × 2 × 13) = 3.7325.
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How to Calculate the Value of the Cube Root of 52?
Cube Root of 52 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 = 52
Let us assume x as 3
[∵ 3^{3} = 27 and 27 is the nearest perfect cube that is less than 52]
⇒ x = 3
Therefore,
∛52 = 3 (3^{3} + 2 × 52)/(2 × 3^{3} + 52)) = 3.71
⇒ ∛52 ≈ 3.71
Therefore, the cube root of 52 is 3.71 approximately.
Is the Cube Root of 52 Irrational?
Yes, because ∛52 = ∛(2 × 2 × 13) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 52 is an irrational number.
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Cube Root of 52 Solved Examples

Example 1: The volume of a spherical ball is 52π in^{3}. What is the radius of this ball?
Solution:
Volume of the spherical ball = 52π in^{3}
= 4/3 × π × R^{3}
⇒ R^{3} = 3/4 × 52
⇒ R = ∛(3/4 × 52) = ∛(3/4) × ∛52 = 0.90856 × 3.73251 (∵ ∛(3/4) = 0.90856 and ∛52 = 3.73251)
⇒ R = 3.39121 in^{3} 
Example 2: Find the real root of the equation x^{3} − 52 = 0.
Solution:
x^{3} − 52 = 0 i.e. x^{3} = 52
Solving for x gives us,
x = ∛52, x = ∛52 × (1 + √3i))/2 and x = ∛52 × (1  √3i))/2
where i is called the imaginary unit and is equal to √1.
Ignoring imaginary roots,
x = ∛52
Therefore, the real root of the equation x^{3} − 52 = 0 is for x = ∛52 = 3.7325.

Example 3: Given the volume of a cube is 52 in^{3}. Find the length of the side of the cube.
Solution:
Volume of the Cube = 52 in^{3} = a^{3}
⇒ a^{3} = 52
Cube rooting on both sides,
⇒ a = ∛52 in
Since the cube root of 52 is 3.73, therefore, the length of the side of the cube is 3.73 in.
FAQs on Cube Root of 52
What is the Value of the Cube Root of 52?
We can express 52 as 2 × 2 × 13 i.e. ∛52 = ∛(2 × 2 × 13) = 3.73251. Therefore, the value of the cube root of 52 is 3.73251.
Is 52 a Perfect Cube?
The number 52 on prime factorization gives 2 × 2 × 13. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 52 is irrational, hence 52 is not a perfect cube.
If the Cube Root of 52 is 3.73, Find the Value of ∛0.052.
Let us represent ∛0.052 in p/q form i.e. ∛(52/1000) = 3.73/10 = 0.37. Hence, the value of ∛0.052 = 0.37.
What is the Value of 3 Plus 11 Cube Root 52?
The value of ∛52 is 3.733. So, 3 + 11 × ∛52 = 3 + 11 × 3.733 = 44.063. Hence, the value of 3 plus 11 cube root 52 is 44.063.
What is the Cube of the Cube Root of 52?
The cube of the cube root of 52 is the number 52 itself i.e. (∛52)^{3} = (52^{1/3})^{3} = 52.
How to Simplify the Cube Root of 52/125?
We know that the cube root of 52 is 3.73251 and the cube root of 125 is 5. Therefore, ∛(52/125) = (∛52)/(∛125) = 3.733/5 = 0.7466.
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