Cube Root of 225
The value of the cube root of 225 rounded to 6 decimal places is 6.082202. It is the real solution of the equation x^{3} = 225. The cube root of 225 is expressed as ∛225 in the radical form and as (225)^{⅓} or (225)^{0.33} in the exponent form. The prime factorization of 225 is 3 × 3 × 5 × 5, hence, the cube root of 225 in its lowest radical form is expressed as ∛225.
 Cube root of 225: 6.082201996
 Cube root of 225 in Exponential Form: (225)^{⅓}
 Cube root of 225 in Radical Form: ∛225
1.  What is the Cube Root of 225? 
2.  How to Calculate the Cube Root of 225? 
3.  Is the Cube Root of 225 Irrational? 
4.  FAQs on Cube Root of 225 
What is the Cube Root of 225?
The cube root of 225 is the number which when multiplied by itself three times gives the product as 225. Since 225 can be expressed as 3 × 3 × 5 × 5. Therefore, the cube root of 225 = ∛(3 × 3 × 5 × 5) = 6.0822.
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How to Calculate the Value of the Cube Root of 225?
Cube Root of 225 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 = 225
Let us assume x as 6
[∵ 6^{3} = 216 and 216 is the nearest perfect cube that is less than 225]
⇒ x = 6
Therefore,
∛225 = 6 (6^{3} + 2 × 225)/(2 × 6^{3} + 225)) = 6.08
⇒ ∛225 ≈ 6.08
Therefore, the cube root of 225 is 6.08 approximately.
Is the Cube Root of 225 Irrational?
Yes, because ∛225 = ∛(3 × 3 × 5 × 5) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 225 is an irrational number.
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Cube Root of 225 Solved Examples

Example 1: The volume of a spherical ball is 225π in^{3}. What is the radius of this ball?
Solution:
Volume of the spherical ball = 225π in^{3}
= 4/3 × π × R^{3}
⇒ R^{3} = 3/4 × 225
⇒ R = ∛(3/4 × 225) = ∛(3/4) × ∛225 = 0.90856 × 6.0822 (∵ ∛(3/4) = 0.90856 and ∛225 = 6.0822)
⇒ R = 5.52604 in^{3} 
Example 2: What is the value of ∛225 + ∛(225)?
Solution:
The cube root of 225 is equal to the negative of the cube root of 225.
i.e. ∛225 = ∛225
Therefore, ∛225 + ∛(225) = ∛225  ∛225 = 0

Example 3: Find the real root of the equation x^{3} − 225 = 0.
Solution:
x^{3} − 225 = 0 i.e. x^{3} = 225
Solving for x gives us,
x = ∛225, x = ∛225 × (1 + √3i))/2 and x = ∛225 × (1  √3i))/2
where i is called the imaginary unit and is equal to √1.
Ignoring imaginary roots,
x = ∛225
Therefore, the real root of the equation x^{3} − 225 = 0 is for x = ∛225 = 6.0822.
FAQs on Cube Root of 225
What is the Value of the Cube Root of 225?
We can express 225 as 3 × 3 × 5 × 5 i.e. ∛225 = ∛(3 × 3 × 5 × 5) = 6.0822. Therefore, the value of the cube root of 225 is 6.0822.
What is the Cube of the Cube Root of 225?
The cube of the cube root of 225 is the number 225 itself i.e. (∛225)^{3} = (225^{1/3})^{3} = 225.
Why is the Value of the Cube Root of 225 Irrational?
The value of the cube root of 225 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛225 is irrational.
What is the Value of 15 Plus 4 Cube Root 225?
The value of ∛225 is 6.082. So, 15 + 4 × ∛225 = 15 + 4 × 6.082 = 39.328. Hence, the value of 15 plus 4 cube root 225 is 39.328.
What is the Cube Root of 225?
The cube root of 225 is equal to the negative of the cube root of 225. Therefore, ∛225 = (∛225) = (6.082) = 6.082.
Is 225 a Perfect Cube?
The number 225 on prime factorization gives 3 × 3 × 5 × 5. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 225 is irrational, hence 225 is not a perfect cube.