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Cube Root of 150

The value of the cube root of 150 rounded to 5 decimal places is 5.31329. It is the real solution of the equation x³ = 150. The cube root of 150 is expressed as ∛150 in the radical form and as (150)^⅓ or (150)^0.33 in the exponent form. The prime factorization of 150 is 2 × 3 × 5 × 5, hence, the cube root of 150 in its lowest radical form is expressed as ∛150.

Cube root of 150: 5.313292846
Cube root of 150 in Exponential Form: (150)^⅓
Cube root of 150 in Radical Form: ∛150

Cube Root of 150

1.	What is the Cube Root of 150?
2.	How to Calculate the Cube Root of 150?
3.	Is the Cube Root of 150 Irrational?
4.	FAQs on Cube Root of 150

What is the Cube Root of 150?

The cube root of 150 is the number which when multiplied by itself three times gives the product as 150. Since 150 can be expressed as 2 × 3 × 5 × 5. Therefore, the cube root of 150 = ∛(2 × 3 × 5 × 5) = 5.3133.

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How to Calculate the Value of the Cube Root of 150?

Cube Root of 150 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 = 150
Let us assume x as 5
[∵ 5³ = 125 and 125 is the nearest perfect cube that is less than 150]
⇒ x = 5
Therefore,
∛150 = 5 (5³ + 2 × 150)/(2 × 5³ + 150)) = 5.31
⇒ ∛150 ≈ 5.31
Therefore, the cube root of 150 is 5.31 approximately.

Is the Cube Root of 150 Irrational?

Yes, because ∛150 = ∛(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 150 is an irrational number.

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Cube Root of 150 Solved Examples

Example 1: What is the value of ∛150 ÷ ∛(-150)?

Solution:

The cube root of -150 is equal to the negative of the cube root of 150.
⇒ ∛-150 = -∛150

Therefore,
⇒ ∛150/∛(-150) = ∛150/(-∛150) = -1
Example 2: The volume of a spherical ball is 150π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 150π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 150
⇒ R = ∛(3/4 × 150) = ∛(3/4) × ∛150 = 0.90856 × 5.31329 (∵ ∛(3/4) = 0.90856 and ∛150 = 5.31329)
⇒ R = 4.82744 in³
Example 3: Find the real root of the equation x³ − 150 = 0.

Solution:

x³ − 150 = 0 i.e. x³ = 150
Solving for x gives us,
x = ∛150, x = ∛150 × (-1 + √3i))/2 and x = ∛150 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛150
Therefore, the real root of the equation x³ − 150 = 0 is for x = ∛150 = 5.3133.

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FAQs on Cube Root of 150

What is the Value of the Cube Root of 150?

We can express 150 as 2 × 3 × 5 × 5 i.e. ∛150 = ∛(2 × 3 × 5 × 5) = 5.31329. Therefore, the value of the cube root of 150 is 5.31329.

If the Cube Root of 150 is 5.31, Find the Value of ∛0.15.

Let us represent ∛0.15 in p/q form i.e. ∛(150/1000) = 5.31/10 = 0.53. Hence, the value of ∛0.15 = 0.53.

What is the Value of 6 Plus 8 Cube Root 150?

The value of ∛150 is 5.313. So, 6 + 8 × ∛150 = 6 + 8 × 5.313 = 48.504. Hence, the value of 6 plus 8 cube root 150 is 48.504.

Is 150 a Perfect Cube?

The number 150 on prime factorization gives 2 × 3 × 5 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 150 is irrational, hence 150 is not a perfect cube.

What is the Cube Root of -150?

The cube root of -150 is equal to the negative of the cube root of 150. Therefore, ∛-150 = -(∛150) = -(5.313) = -5.313.

How to Simplify the Cube Root of 150/343?

We know that the cube root of 150 is 5.31329 and the cube root of 343 is 7. Therefore, ∛(150/343) = (∛150)/(∛343) = 5.313/7 = 0.759.

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