A day full of math games & activities. Find one near you.

Cube Root of 500

The value of the cube root of 500 rounded to 6 decimal places is 7.937005. It is the real solution of the equation x³ = 500. The cube root of 500 is expressed as ∛500 or 5 ∛4 in the radical form and as (500)^⅓ or (500)^0.33 in the exponent form. The prime factorization of 500 is 2 × 2 × 5 × 5 × 5, hence, the cube root of 500 in its lowest radical form is expressed as 5 ∛4.

Cube root of 500: 7.93700526
Cube root of 500 in Exponential Form: (500)^⅓
Cube root of 500 in Radical Form: ∛500 or 5 ∛4

Cube Root of 500

1.	What is the Cube Root of 500?
2.	How to Calculate the Cube Root of 500?
3.	Is the Cube Root of 500 Irrational?
4.	FAQs on Cube Root of 500

What is the Cube Root of 500?

The cube root of 500 is the number which when multiplied by itself three times gives the product as 500. Since 500 can be expressed as 2 × 2 × 5 × 5 × 5. Therefore, the cube root of 500 = ∛(2 × 2 × 5 × 5 × 5) = 7.937.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 500?

Cube Root of 500 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 = 500
Let us assume x as 7
[∵ 7³ = 343 and 343 is the nearest perfect cube that is less than 500]
⇒ x = 7
Therefore,
∛500 = 7 (7³ + 2 × 500)/(2 × 7³ + 500)) = 7.93
⇒ ∛500 ≈ 7.93
Therefore, the cube root of 500 is 7.93 approximately.

Is the Cube Root of 500 Irrational?

Yes, because ∛500 = ∛(2 × 2 × 5 × 5 × 5) = 5 ∛4 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 500 is an irrational number.

☛ Also Check:

Cube Root of 500 Solved Examples

Example 1: The volume of a spherical ball is 500π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 500π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 500
⇒ R = ∛(3/4 × 500) = ∛(3/4) × ∛500 = 0.90856 × 7.93701 (∵ ∛(3/4) = 0.90856 and ∛500 = 7.93701)
⇒ R = 7.21125 in³
Example 2: What is the value of ∛500 + ∛(-500)?

Solution:

The cube root of -500 is equal to the negative of the cube root of 500.
i.e. ∛-500 = -∛500

Therefore, ∛500 + ∛(-500) = ∛500 - ∛500 = 0
Example 3: Find the real root of the equation x³ − 500 = 0.

Solution:

x³ − 500 = 0 i.e. x³ = 500
Solving for x gives us,
x = ∛500, x = ∛500 × (-1 + √3i))/2 and x = ∛500 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛500
Therefore, the real root of the equation x³ − 500 = 0 is for x = ∛500 = 7.937.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on Cube Root of 500

What is the Value of the Cube Root of 500?

We can express 500 as 2 × 2 × 5 × 5 × 5 i.e. ∛500 = ∛(2 × 2 × 5 × 5 × 5) = 7.93701. Therefore, the value of the cube root of 500 is 7.93701.

What is the Cube of the Cube Root of 500?

The cube of the cube root of 500 is the number 500 itself i.e. (∛500)³ = (500^1/3)³ = 500.

Is 500 a Perfect Cube?

The number 500 on prime factorization gives 2 × 2 × 5 × 5 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 500 is irrational, hence 500 is not a perfect cube.

Why is the Value of the Cube Root of 500 Irrational?

The value of the cube root of 500 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛500 is irrational.

How to Simplify the Cube Root of 500/729?

We know that the cube root of 500 is 7.93701 and the cube root of 729 is 9. Therefore, ∛(500/729) = (∛500)/(∛729) = 7.937/9 = 0.8819.

What is the Cube Root of -500?

The cube root of -500 is equal to the negative of the cube root of 500. Therefore, ∛-500 = -(∛500) = -(7.937) = -7.937.

Math worksheets and
visual curriculum