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Cube Root of 300

The value of the cube root of 300 rounded to 7 decimal places is 6.6943295. It is the real solution of the equation x³ = 300. The cube root of 300 is expressed as ∛300 in the radical form and as (300)^⅓ or (300)^0.33 in the exponent form. The prime factorization of 300 is 2 × 2 × 3 × 5 × 5, hence, the cube root of 300 in its lowest radical form is expressed as ∛300.

Cube root of 300: 6.694329501
Cube root of 300 in Exponential Form: (300)^⅓
Cube root of 300 in Radical Form: ∛300

Cube Root of 300

1.	What is the Cube Root of 300?
2.	How to Calculate the Cube Root of 300?
3.	Is the Cube Root of 300 Irrational?
4.	FAQs on Cube Root of 300

What is the Cube Root of 300?

The cube root of 300 is the number which when multiplied by itself three times gives the product as 300. Since 300 can be expressed as 2 × 2 × 3 × 5 × 5. Therefore, the cube root of 300 = ∛(2 × 2 × 3 × 5 × 5) = 6.6943.

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How to Calculate the Value of the Cube Root of 300?

Cube Root of 300 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 = 300
Let us assume x as 6
[∵ 6³ = 216 and 216 is the nearest perfect cube that is less than 300]
⇒ x = 6
Therefore,
∛300 = 6 (6³ + 2 × 300)/(2 × 6³ + 300)) = 6.69
⇒ ∛300 ≈ 6.69
Therefore, the cube root of 300 is 6.69 approximately.

Is the Cube Root of 300 Irrational?

Yes, because ∛300 = ∛(2 × 2 × 3 × 5 × 5) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 300 is an irrational number.

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Cube Root of 300 Solved Examples

Example 1: Find the real root of the equation x³ − 300 = 0.

Solution:

x³ − 300 = 0 i.e. x³ = 300
Solving for x gives us,
x = ∛300, x = ∛300 × (-1 + √3i))/2 and x = ∛300 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛300
Therefore, the real root of the equation x³ − 300 = 0 is for x = ∛300 = 6.6943.
Example 2: Given the volume of a cube is 300 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 300 in³ = a³
⇒ a³ = 300
Cube rooting on both sides,
⇒ a = ∛300 in
Since the cube root of 300 is 6.69, therefore, the length of the side of the cube is 6.69 in.
Example 3: What is the value of ∛300 ÷ ∛(-300)?

Solution:

The cube root of -300 is equal to the negative of the cube root of 300.
⇒ ∛-300 = -∛300

Therefore,
⇒ ∛300/∛(-300) = ∛300/(-∛300) = -1

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FAQs on Cube Root of 300

What is the Value of the Cube Root of 300?

We can express 300 as 2 × 2 × 3 × 5 × 5 i.e. ∛300 = ∛(2 × 2 × 3 × 5 × 5) = 6.69433. Therefore, the value of the cube root of 300 is 6.69433.

What is the Value of 1 Plus 8 Cube Root 300?

The value of ∛300 is 6.694. So, 1 + 8 × ∛300 = 1 + 8 × 6.694 = 54.552. Hence, the value of 1 plus 8 cube root 300 is 54.552.

Why is the Value of the Cube Root of 300 Irrational?

The value of the cube root of 300 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛300 is irrational.

Is 300 a Perfect Cube?

The number 300 on prime factorization gives 2 × 2 × 3 × 5 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 300 is irrational, hence 300 is not a perfect cube.

What is the Cube Root of -300?

The cube root of -300 is equal to the negative of the cube root of 300. Therefore, ∛-300 = -(∛300) = -(6.694) = -6.694.

What is the Cube of the Cube Root of 300?

The cube of the cube root of 300 is the number 300 itself i.e. (∛300)³ = (300^1/3)³ = 300.

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