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Cube Root of 529

The value of the cube root of 529 rounded to 6 decimal places is 8.087579. It is the real solution of the equation x³ = 529. The cube root of 529 is expressed as ∛529 in the radical form and as (529)^⅓ or (529)^0.33 in the exponent form. The prime factorization of 529 is 23 × 23, hence, the cube root of 529 in its lowest radical form is expressed as ∛529.

Cube root of 529: 8.087579399
Cube root of 529 in Exponential Form: (529)^⅓
Cube root of 529 in Radical Form: ∛529

1.	What is the Cube Root of 529?
2.	How to Calculate the Cube Root of 529?
3.	Is the Cube Root of 529 Irrational?
4.	FAQs on Cube Root of 529

What is the Cube Root of 529?

The cube root of 529 is the number which when multiplied by itself three times gives the product as 529. Since 529 can be expressed as 23 × 23. Therefore, the cube root of 529 = ∛(23 × 23) = 8.0876.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 529?

Cube Root of 529 by Halley's Method

Its formula is ∛a ≈ x ((x³ + 2a)/(2x³ + a))
where,
a = number whose cube root is being calculated
x = integer guess of its cube root.

Here a = 529
Let us assume x as 8
[∵ 8³ = 512 and 512 is the nearest perfect cube that is less than 529]
⇒ x = 8
Therefore,
∛529 = 8 (8³ + 2 × 529)/(2 × 8³ + 529)) = 8.09
⇒ ∛529 ≈ 8.09
Therefore, the cube root of 529 is 8.09 approximately.

Is the Cube Root of 529 Irrational?

Yes, because ∛529 = ∛(23 × 23) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 529 is an irrational number.

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Cube Root of 529 Solved Examples

Example 1: The volume of a spherical ball is 529π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 529π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 529
⇒ R = ∛(3/4 × 529) = ∛(3/4) × ∛529 = 0.90856 × 8.08758 (∵ ∛(3/4) = 0.90856 and ∛529 = 8.08758)
⇒ R = 7.34805 in³
Example 2: What is the value of ∛529 + ∛(-529)?

Solution:

The cube root of -529 is equal to the negative of the cube root of 529.
i.e. ∛-529 = -∛529

Therefore, ∛529 + ∛(-529) = ∛529 - ∛529 = 0
Example 3: Given the volume of a cube is 529 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 529 in³ = a³
⇒ a³ = 529
Cube rooting on both sides,
⇒ a = ∛529 in
Since the cube root of 529 is 8.09, therefore, the length of the side of the cube is 8.09 in.

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FAQs on Cube Root of 529

What is the Value of the Cube Root of 529?

We can express 529 as 23 × 23 i.e. ∛529 = ∛(23 × 23) = 8.08758. Therefore, the value of the cube root of 529 is 8.08758.

What is the Value of 6 Plus 2 Cube Root 529?

The value of ∛529 is 8.088. So, 6 + 2 × ∛529 = 6 + 2 × 8.088 = 22.176. Hence, the value of 6 plus 2 cube root 529 is 22.176.

What is the Cube of the Cube Root of 529?

The cube of the cube root of 529 is the number 529 itself i.e. (∛529)³ = (529^1/3)³ = 529.

If the Cube Root of 529 is 8.09, Find the Value of ∛0.529.

Let us represent ∛0.529 in p/q form i.e. ∛(529/1000) = 8.09/10 = 0.81. Hence, the value of ∛0.529 = 0.81.

What is the Cube Root of -529?

The cube root of -529 is equal to the negative of the cube root of 529. Therefore, ∛-529 = -(∛529) = -(8.088) = -8.088.

How to Simplify the Cube Root of 529/729?

We know that the cube root of 529 is 8.08758 and the cube root of 729 is 9. Therefore, ∛(529/729) = (∛529)/(∛729) = 8.088/9 = 0.8987.