Cube Root of 15

The value of the cube root of 15 rounded to 7 decimal places is 2.4662121. It is the real solution of the equation x³ = 15. The cube root of 15 is expressed as ∛15 in the radical form and as (15)^⅓ or (15)^0.33 in the exponent form. The prime factorization of 15 is 3 × 5, hence, the cube root of 15 in its lowest radical form is expressed as ∛15.

Cube root of 15: 2.466212074
Cube root of 15 in Exponential Form: (15)^⅓
Cube root of 15 in Radical Form: ∛15

Cube Root of 15

1.	What is the Cube Root of 15?
2.	How to Calculate the Cube Root of 15?
3.	Is the Cube Root of 15 Irrational?
4.	FAQs on Cube Root of 15

What is the Cube Root of 15?

The cube root of 15 is the number which when multiplied by itself three times gives the product as 15. Since 15 can be expressed as 3 × 5. Therefore, the cube root of 15 = ∛(3 × 5) = 2.4662.

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How to Calculate the Value of the Cube Root of 15?

Cube Root of 15 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 = 15
Let us assume x as 2
[∵ 2³ = 8 and 8 is the nearest perfect cube that is less than 15]
⇒ x = 2
Therefore,
∛15 = 2 (2³ + 2 × 15)/(2 × 2³ + 15)) = 2.45
⇒ ∛15 ≈ 2.45
Therefore, the cube root of 15 is 2.45 approximately.

Is the Cube Root of 15 Irrational?

Yes, because ∛15 = ∛(3 × 5) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 15 is an irrational number.

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Cube Root of 15 Solved Examples

Example 1: Find the real root of the equation x³ − 15 = 0.

Solution:

x³ − 15 = 0 i.e. x³ = 15
Solving for x gives us,
x = ∛15, x = ∛15 × (-1 + √3i))/2 and x = ∛15 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛15
Therefore, the real root of the equation x³ − 15 = 0 is for x = ∛15 = 2.4662.
Example 2: The volume of a spherical ball is 15π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 15π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 15
⇒ R = ∛(3/4 × 15) = ∛(3/4) × ∛15 = 0.90856 × 2.46621 (∵ ∛(3/4) = 0.90856 and ∛15 = 2.46621)
⇒ R = 2.2407 in³
Example 3: What is the value of ∛15 ÷ ∛(-15)?

Solution:

The cube root of -15 is equal to the negative of the cube root of 15.
⇒ ∛-15 = -∛15

Therefore,
⇒ ∛15/∛(-15) = ∛15/(-∛15) = -1

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FAQs on Cube Root of 15

What is the Value of the Cube Root of 15?

We can express 15 as 3 × 5 i.e. ∛15 = ∛(3 × 5) = 2.46621. Therefore, the value of the cube root of 15 is 2.46621.

What is the Cube of the Cube Root of 15?

The cube of the cube root of 15 is the number 15 itself i.e. (∛15)³ = (15^1/3)³ = 15.

Why is the Value of the Cube Root of 15 Irrational?

The value of the cube root of 15 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛15 is irrational.

How to Simplify the Cube Root of 15/216?

We know that the cube root of 15 is 2.46621 and the cube root of 216 is 6. Therefore, ∛(15/216) = (∛15)/(∛216) = 2.466/6 = 0.411.

What is the Value of 15 Plus 11 Cube Root 15?

The value of ∛15 is 2.466. So, 15 + 11 × ∛15 = 15 + 11 × 2.466 = 42.126000000000005. Hence, the value of 15 plus 11 cube root 15 is 42.126000000000005.

Is 15 a Perfect Cube?

The number 15 on prime factorization gives 3 × 5. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 15 is irrational, hence 15 is not a perfect cube.

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