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Cube Root of 1728
The value of the cube root of 1728 is 12. It is the real solution of the equation x^{3} = 1728. The cube root of 1728 is expressed as ∛1728 in radical form and as (1728)^{⅓} or (1728)^{0.33} in the exponent form. As the cube root of 1728 is a whole number, 1728 is a perfect cube.
 Cube root of 1728: 12
 Cube root of 1728 in exponential form: (1728)^{⅓}
 Cube root of 1728 in radical form: ∛1728
1.  What is the Cube Root of 1728? 
2.  How to Calculate the Cube Root of 1728? 
3.  Is the Cube Root of 1728 Irrational? 
4.  FAQs on Cube Root of 1728 
What is the Cube Root of 1728?
The cube root of 1728 is the number which when multiplied by itself three times gives the product as 1728. Since 1728 can be expressed as 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3. Therefore, the cube root of 1728 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) = 12.
How to Calculate the Value of the Cube Root of 1728?
Cube Root of 1728 by Prime Factorization
 Prime factorization of 1728 is 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
 Simplifying the above expression: 2^{6} × 3^{3}
 Simplifying further: 12^{3}
Therefore, the cube root of 1728 by prime factorization is (2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3)^{1/3} = 12.
Is the Cube Root of 1728 Irrational?
No, because ∛1728 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) can be expressed in the form of p/q i.e. 12/1. Therefore, the value of the cube root of 1728 is an integer (rational).
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Cube Root of 1728 Solved Examples

Example 1: The volume of a spherical ball is 1728π in^{3}. What is the radius of this ball?
Solution:
Volume of the spherical ball = 1728π in^{3}
= 4/3 × π × R^{3}
⇒ R^{3} = 3/4 × 1728
⇒ R = ∛(3/4 × 1728) = ∛(3/4) × ∛1728 = 0.90856 × 12 (∵ ∛(3/4) = 0.90856 and ∛1728 = 12)
⇒ R = 10.90272 in^{3} 
Example 2: What is the value of ∛1728 ÷ ∛(1728)?
Solution:
The cube root of 1728 is equal to the negative of the cube root of 1728.
⇒ ∛1728 = ∛1728
Therefore,
⇒ ∛1728/∛(1728) = ∛1728/(∛1728) = 1 
Example 3: Find the real root of the equation x^{3} − 1728 = 0.
Solution:
x^{3} − 1728 = 0 i.e. x^{3} = 1728
Solving for x gives us,
x = ∛1728, x = ∛1728 × (1 + √3i))/2 and x = ∛1728 × (1  √3i))/2
where i is called the imaginary unit and is equal to √1.
Ignoring imaginary roots,
x = ∛1728
Therefore, the real root of the equation x^{3} − 1728 = 0 is for x = ∛1728 = 12.
FAQs on Cube Root of 1728
What is the Value of the Cube Root of 1728?
We can express 1728 as 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 i.e. ∛1728 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) = 12. Therefore, the value of the cube root of 1728 is 12.
Is 1728 a Perfect Cube?
The number 1728 on prime factorization gives 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3. On combining the prime factors in groups of 3 gives 12. So, the cube root of 1728 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) = 12 (perfect cube).
If the Cube Root of 1728 is 12, Find the Value of ∛1.728.
Let us represent ∛1.728 in p/q form i.e. ∛(1728/1000) = 12/10 = 1.2. Hence, the value of ∛1.728 = 1.2.
What is the Cube of the Cube Root of 1728?
The cube of the cube root of 1728 is the number 1728 itself i.e. (∛1728)^{3} = (1728^{1/3})^{3} = 1728.
What is the Value of 14 Plus 20 Cube Root 1728?
The value of ∛1728 is 12. So, 14 + 20 × ∛1728 = 14 + 20 × 12 = 254. Hence, the value of 14 plus 20 cube root 1728 is 254.
Why is the value of the Cube Root of 1728 Rational?
The value of the cube root of 1728 can be expressed in the form of p/q i.e. = 12/1, where q ≠ 0. Therefore, the ∛1728 is rational.
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