Cube Root of 729
The value of the cube root of 729 is 9. It is the real solution of the equation x^{3} = 729. The cube root of 729 is expressed as ∛729 in radical form and as (729)^{⅓} or (729)^{0.33} in the exponent form. As the cube root of 729 is a whole number, 729 is a perfect cube.
 Cube root of 729: 9
 Cube root of 729 in exponential form: (729)^{⅓}
 Cube root of 729 in radical form: ∛729
1.  What is the Cube Root of 729? 
2.  How to Calculate the Cube Root of 729? 
3.  Is the Cube Root of 729 Irrational? 
4.  FAQs on Cube Root of 729 
What is the Cube Root of 729?
The cube root of 729 is the number which when multiplied by itself three times gives the product as 729. Since 729 can be expressed as 3 × 3 × 3 × 3 × 3 × 3. Therefore, the cube root of 729 = ∛(3 × 3 × 3 × 3 × 3 × 3) = 9.
How to Calculate the Value of the Cube Root of 729?
Cube Root of 729 by Prime Factorization
 Prime factorization of 729 is 3 × 3 × 3 × 3 × 3 × 3
 Simplifying the above expression: 3^{6}
 Simplifying further: 9^{3}
Therefore, the cube root of 729 by prime factorization is (3 × 3 × 3 × 3 × 3 × 3)^{1/3} = 9.
Is the Cube Root of 729 Irrational?
No, because ∛729 = ∛(3 × 3 × 3 × 3 × 3 × 3) can be expressed in the form of p/q i.e. 9/1. Therefore, the value of the cube root of 729 is an integer (rational).
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Cube Root of 729 Solved Examples

Example 1: What is the value of ∛729 ÷ ∛(729)?
Solution:
The cube root of 729 is equal to the negative of the cube root of 729.
⇒ ∛729 = ∛729
Therefore,
⇒ ∛729/∛(729) = ∛729/(∛729) = 1 
Example 2: Given the volume of a cube is 729 in^{3}. Find the length of the side of the cube.
Solution:
Volume of the Cube = 729 in^{3} = a^{3}
⇒ a^{3} = 729
Cube rooting on both sides,
⇒ a = ∛729 in
Since the cube root of 729 is 9, therefore, the length of the side of the cube is 9 in. 
Example 3: Find the real root of the equation x^{3} − 729 = 0.
Solution:
x^{3} − 729 = 0 i.e. x^{3} = 729
Solving for x gives us,
x = ∛729, x = ∛729 × (1 + √3i))/2 and x = ∛729 × (1  √3i))/2
where i is called the imaginary unit and is equal to √1.
Ignoring imaginary roots,
x = ∛729
Therefore, the real root of the equation x^{3} − 729 = 0 is for x = ∛729 = 9.
FAQs on Cube Root of 729
What is the Value of the Cube Root of 729?
We can express 729 as 3 × 3 × 3 × 3 × 3 × 3 i.e. ∛729 = ∛(3 × 3 × 3 × 3 × 3 × 3) = 9. Therefore, the value of the cube root of 729 is 9.
What is the Cube Root of 729?
The cube root of 729 is equal to the negative of the cube root of 729. Therefore, ∛729 = (∛729) = (9) = 9.
If the Cube Root of 729 is 9, Find the Value of ∛0.729.
Let us represent ∛0.729 in p/q form i.e. ∛(729/1000) = 9/10 = 0.9. Hence, the value of ∛0.729 = 0.9.
Is 729 a Perfect Cube?
The number 729 on prime factorization gives 3 × 3 × 3 × 3 × 3 × 3. On combining the prime factors in groups of 3 gives 9. So, the cube root of 729 = ∛(3 × 3 × 3 × 3 × 3 × 3) = 9 (perfect cube).
Why is the value of the Cube Root of 729 Rational?
The value of the cube root of 729 can be expressed in the form of p/q i.e. = 9/1, where q ≠ 0. Therefore, the ∛729 is rational.
What is the Cube of the Cube Root of 729?
The cube of the cube root of 729 is the number 729 itself i.e. (∛729)^{3} = (729^{1/3})^{3} = 729.