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Cube Root of 729

The value of the cube root of 729 is 9. It is the real solution of the equation x3 = 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

Cube Root of 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: 36
  • Simplifying further: 93

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

  1. 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

  2. Example 2: Given the volume of a cube is 729 in3. Find the length of the side of the cube.

    Solution:

    Volume of the Cube = 729 in3 = a3
    ⇒ a3 = 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.

  3. Example 3: Find the real root of the equation x3 − 729 = 0.

    Solution:

    x3 − 729 = 0 i.e. x3 = 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 x3 − 729 = 0 is for x = ∛729 = 9.

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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 = (7291/3)3 = 729.

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