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Cube Root of 320

The value of the cube root of 320 rounded to 4 decimal places is 6.8399. It is the real solution of the equation x³ = 320. The cube root of 320 is expressed as ∛320 or 4 ∛5 in the radical form and as (320)^⅓ or (320)^0.33 in the exponent form. The prime factorization of 320 is 2 × 2 × 2 × 2 × 2 × 2 × 5, hence, the cube root of 320 in its lowest radical form is expressed as 4 ∛5.

Cube root of 320: 6.839903787
Cube root of 320 in Exponential Form: (320)^⅓
Cube root of 320 in Radical Form: ∛320 or 4 ∛5

1.	What is the Cube Root of 320?
2.	How to Calculate the Cube Root of 320?
3.	Is the Cube Root of 320 Irrational?
4.	FAQs on Cube Root of 320

What is the Cube Root of 320?

The cube root of 320 is the number which when multiplied by itself three times gives the product as 320. Since 320 can be expressed as 2 × 2 × 2 × 2 × 2 × 2 × 5. Therefore, the cube root of 320 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 5) = 6.8399.

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How to Calculate the Value of the Cube Root of 320?

Cube Root of 320 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 = 320
Let us assume x as 6
[∵ 6³ = 216 and 216 is the nearest perfect cube that is less than 320]
⇒ x = 6
Therefore,
∛320 = 6 (6³ + 2 × 320)/(2 × 6³ + 320)) = 6.83
⇒ ∛320 ≈ 6.83
Therefore, the cube root of 320 is 6.83 approximately.

Is the Cube Root of 320 Irrational?

Yes, because ∛320 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 5) = 4 ∛5 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 320 is an irrational number.

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Cube Root of 320 Solved Examples

Example 1: The volume of a spherical ball is 320π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 320π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 320
⇒ R = ∛(3/4 × 320) = ∛(3/4) × ∛320 = 0.90856 × 6.8399 (∵ ∛(3/4) = 0.90856 and ∛320 = 6.8399)
⇒ R = 6.21446 in³
Example 2: Given the volume of a cube is 320 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 320 in³ = a³
⇒ a³ = 320
Cube rooting on both sides,
⇒ a = ∛320 in
Since the cube root of 320 is 6.84, therefore, the length of the side of the cube is 6.84 in.
Example 3: What is the value of ∛320 ÷ ∛(-320)?

Solution:

The cube root of -320 is equal to the negative of the cube root of 320.
⇒ ∛-320 = -∛320

Therefore,
⇒ ∛320/∛(-320) = ∛320/(-∛320) = -1

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FAQs on Cube Root of 320

What is the Value of the Cube Root of 320?

We can express 320 as 2 × 2 × 2 × 2 × 2 × 2 × 5 i.e. ∛320 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 5) = 6.8399. Therefore, the value of the cube root of 320 is 6.8399.

Is 320 a Perfect Cube?

The number 320 on prime factorization gives 2 × 2 × 2 × 2 × 2 × 2 × 5. Here, the prime factor 5 is not in the power of 3. Therefore the cube root of 320 is irrational, hence 320 is not a perfect cube.

What is the Cube Root of -320?

The cube root of -320 is equal to the negative of the cube root of 320. Therefore, ∛-320 = -(∛320) = -(6.84) = -6.84.

How to Simplify the Cube Root of 320/216?

We know that the cube root of 320 is 6.8399 and the cube root of 216 is 6. Therefore, ∛(320/216) = (∛320)/(∛216) = 6.84/6 = 1.14.

What is the Cube of the Cube Root of 320?

The cube of the cube root of 320 is the number 320 itself i.e. (∛320)³ = (320^1/3)³ = 320.

What is the Value of 14 Plus 20 Cube Root 320?

The value of ∛320 is 6.84. So, 14 + 20 × ∛320 = 14 + 20 × 6.84 = 150.8. Hence, the value of 14 plus 20 cube root 320 is 150.8.