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Cube Root of 800

The value of the cube root of 800 rounded to 4 decimal places is 9.2832. It is the real solution of the equation x³ = 800. The cube root of 800 is expressed as ∛800 or 2 ∛100 in the radical form and as (800)^⅓ or (800)^0.33 in the exponent form. The prime factorization of 800 is 2 × 2 × 2 × 2 × 2 × 5 × 5, hence, the cube root of 800 in its lowest radical form is expressed as 2 ∛100.

Cube root of 800: 9.283177667
Cube root of 800 in Exponential Form: (800)^⅓
Cube root of 800 in Radical Form: ∛800 or 2 ∛100

Cube Root of 800

1.	What is the Cube Root of 800?
2.	How to Calculate the Cube Root of 800?
3.	Is the Cube Root of 800 Irrational?
4.	FAQs on Cube Root of 800

What is the Cube Root of 800?

The cube root of 800 is the number which when multiplied by itself three times gives the product as 800. Since 800 can be expressed as 2 × 2 × 2 × 2 × 2 × 5 × 5. Therefore, the cube root of 800 = ∛(2 × 2 × 2 × 2 × 2 × 5 × 5) = 9.2832.

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How to Calculate the Value of the Cube Root of 800?

Cube Root of 800 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 = 800
Let us assume x as 9
[∵ 9³ = 729 and 729 is the nearest perfect cube that is less than 800]
⇒ x = 9
Therefore,
∛800 = 9 (9³ + 2 × 800)/(2 × 9³ + 800)) = 9.28
⇒ ∛800 ≈ 9.28
Therefore, the cube root of 800 is 9.28 approximately.

Is the Cube Root of 800 Irrational?

Yes, because ∛800 = ∛(2 × 2 × 2 × 2 × 2 × 5 × 5) = 2 ∛100 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 800 is an irrational number.

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Cube Root of 800 Solved Examples

Example 1: The volume of a spherical ball is 800π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 800π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 800
⇒ R = ∛(3/4 × 800) = ∛(3/4) × ∛800 = 0.90856 × 9.28318 (∵ ∛(3/4) = 0.90856 and ∛800 = 9.28318)
⇒ R = 8.43433 in³
Example 2: Find the real root of the equation x³ − 800 = 0.

Solution:

x³ − 800 = 0 i.e. x³ = 800
Solving for x gives us,
x = ∛800, x = ∛800 × (-1 + √3i))/2 and x = ∛800 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛800
Therefore, the real root of the equation x³ − 800 = 0 is for x = ∛800 = 9.2832.
Example 3: Given the volume of a cube is 800 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 800 in³ = a³
⇒ a³ = 800
Cube rooting on both sides,
⇒ a = ∛800 in
Since the cube root of 800 is 9.28, therefore, the length of the side of the cube is 9.28 in.

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FAQs on Cube Root of 800

What is the Value of the Cube Root of 800?

We can express 800 as 2 × 2 × 2 × 2 × 2 × 5 × 5 i.e. ∛800 = ∛(2 × 2 × 2 × 2 × 2 × 5 × 5) = 9.28318. Therefore, the value of the cube root of 800 is 9.28318.

What is the Value of 4 Plus 4 Cube Root 800?

The value of ∛800 is 9.283. So, 4 + 4 × ∛800 = 4 + 4 × 9.283 = 41.132. Hence, the value of 4 plus 4 cube root 800 is 41.132.

What is the Cube Root of -800?

The cube root of -800 is equal to the negative of the cube root of 800. Therefore, ∛-800 = -(∛800) = -(9.283) = -9.283.

If the Cube Root of 800 is 9.28, Find the Value of ∛0.8.

Let us represent ∛0.8 in p/q form i.e. ∛(800/1000) = 9.28/10 = 0.93. Hence, the value of ∛0.8 = 0.93.

What is the Cube of the Cube Root of 800?

The cube of the cube root of 800 is the number 800 itself i.e. (∛800)³ = (800^1/3)³ = 800.

Why is the Value of the Cube Root of 800 Irrational?

The value of the cube root of 800 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛800 is irrational.

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