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Cube Root of 16

The value of the cube root of 16 rounded to 5 decimal places is 2.51984. It is the real solution of the equation x³ = 16. The cube root of 16 is expressed as ∛16 or 2 ∛2 in the radical form and as (16)^⅓ or (16)^0.33 in the exponent form. The prime factorization of 16 is 2 × 2 × 2 × 2, hence, the cube root of 16 in its lowest radical form is expressed as 2 ∛2.

Cube root of 16: 2.5198421
Cube root of 16 in Exponential Form: (16)^⅓
Cube root of 16 in Radical Form: ∛16 or 2 ∛2

Cube Root of 16

1.	What is the Cube Root of 16?
2.	How to Calculate the Cube Root of 16?
3.	Is the Cube Root of 16 Irrational?
4.	FAQs on Cube Root of 16

What is the Cube Root of 16?

The cube root of 16 is the number which when multiplied by itself three times gives the product as 16. Since 16 can be expressed as 2 × 2 × 2 × 2. Therefore, the cube root of 16 = ∛(2 × 2 × 2 × 2) = 2.5198.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 16?

Cube Root of 16 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 = 16
Let us assume x as 2
[∵ 2³ = 8 and 8 is the nearest perfect cube that is less than 16]
⇒ x = 2
Therefore,
∛16 = 2 (2³ + 2 × 16)/(2 × 2³ + 16)) = 2.5
⇒ ∛16 ≈ 2.5
Therefore, the cube root of 16 is 2.5 approximately.

Is the Cube Root of 16 Irrational?

Yes, because ∛16 = ∛(2 × 2 × 2 × 2) = 2 ∛2 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 16 is an irrational number.

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Cube Root of 16 Solved Examples

Example 1: What is the value of ∛16 ÷ ∛(-16)?

Solution:

The cube root of -16 is equal to the negative of the cube root of 16.
⇒ ∛-16 = -∛16

Therefore,
⇒ ∛16/∛(-16) = ∛16/(-∛16) = -1
Example 2: The volume of a spherical ball is 16π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 16π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 16
⇒ R = ∛(3/4 × 16) = ∛(3/4) × ∛16 = 0.90856 × 2.51984 (∵ ∛(3/4) = 0.90856 and ∛16 = 2.51984)
⇒ R = 2.28943 in³
Example 3: Find the real root of the equation x³ − 16 = 0.

Solution:

x³ − 16 = 0 i.e. x³ = 16
Solving for x gives us,
x = ∛16, x = ∛16 × (-1 + √3i))/2 and x = ∛16 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛16
Therefore, the real root of the equation x³ − 16 = 0 is for x = ∛16 = 2.5198.

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FAQs on Cube Root of 16

What is the Value of the Cube Root of 16?

We can express 16 as 2 × 2 × 2 × 2 i.e. ∛16 = ∛(2 × 2 × 2 × 2) = 2.51984. Therefore, the value of the cube root of 16 is 2.51984.

Why is the Value of the Cube Root of 16 Irrational?

The value of the cube root of 16 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛16 is irrational.

What is the Cube of the Cube Root of 16?

The cube of the cube root of 16 is the number 16 itself i.e. (∛16)³ = (16^1/3)³ = 16.

How to Simplify the Cube Root of 16/512?

We know that the cube root of 16 is 2.51984 and the cube root of 512 is 8. Therefore, ∛(16/512) = (∛16)/(∛512) = 2.52/8 = 0.315.

If the Cube Root of 16 is 2.52, Find the Value of ∛0.016.

Let us represent ∛0.016 in p/q form i.e. ∛(16/1000) = 2.52/10 = 0.25. Hence, the value of ∛0.016 = 0.25.

What is the Cube Root of -16?

The cube root of -16 is equal to the negative of the cube root of 16. Therefore, ∛-16 = -(∛16) = -(2.52) = -2.52.

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