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Cube Root of 32

The value of the cube root of 32 rounded to 4 decimal places is 3.1748. It is the real solution of the equation x³ = 32. The cube root of 32 is expressed as ∛32 or 2 ∛4 in the radical form and as (32)^⅓ or (32)^0.33 in the exponent form. The prime factorization of 32 is 2 × 2 × 2 × 2 × 2, hence, the cube root of 32 in its lowest radical form is expressed as 2 ∛4.

Cube root of 32: 3.174802104
Cube root of 32 in Exponential Form: (32)^⅓
Cube root of 32 in Radical Form: ∛32 or 2 ∛4

Cube Root of 32

1.	What is the Cube Root of 32?
2.	How to Calculate the Cube Root of 32?
3.	Is the Cube Root of 32 Irrational?
4.	FAQs on Cube Root of 32

What is the Cube Root of 32?

The cube root of 32 is the number which when multiplied by itself three times gives the product as 32. Since 32 can be expressed as 2 × 2 × 2 × 2 × 2. Therefore, the cube root of 32 = ∛(2 × 2 × 2 × 2 × 2) = 3.1748.

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How to Calculate the Value of the Cube Root of 32?

Cube Root of 32 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 = 32
Let us assume x as 3
[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 32]
⇒ x = 3
Therefore,
∛32 = 3 (3³ + 2 × 32)/(2 × 3³ + 32)) = 3.17
⇒ ∛32 ≈ 3.17
Therefore, the cube root of 32 is 3.17 approximately.

Is the Cube Root of 32 Irrational?

Yes, because ∛32 = ∛(2 × 2 × 2 × 2 × 2) = 2 ∛4 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 32 is an irrational number.

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Cube Root of 32 Solved Examples

Example 1: The volume of a spherical ball is 32π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 32π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 32
⇒ R = ∛(3/4 × 32) = ∛(3/4) × ∛32 = 0.90856 × 3.1748 (∵ ∛(3/4) = 0.90856 and ∛32 = 3.1748)
⇒ R = 2.8845 in³
Example 2: What is the value of ∛32 + ∛(-32)?

Solution:

The cube root of -32 is equal to the negative of the cube root of 32.
i.e. ∛-32 = -∛32

Therefore, ∛32 + ∛(-32) = ∛32 - ∛32 = 0
Example 3: Find the real root of the equation x³ − 32 = 0.

Solution:

x³ − 32 = 0 i.e. x³ = 32
Solving for x gives us,
x = ∛32, x = ∛32 × (-1 + √3i))/2 and x = ∛32 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛32
Therefore, the real root of the equation x³ − 32 = 0 is for x = ∛32 = 3.1748.

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FAQs on Cube Root of 32

What is the Value of the Cube Root of 32?

We can express 32 as 2 × 2 × 2 × 2 × 2 i.e. ∛32 = ∛(2 × 2 × 2 × 2 × 2) = 3.1748. Therefore, the value of the cube root of 32 is 3.1748.

What is the Cube of the Cube Root of 32?

The cube of the cube root of 32 is the number 32 itself i.e. (∛32)³ = (32^1/3)³ = 32.

Why is the Value of the Cube Root of 32 Irrational?

The value of the cube root of 32 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛32 is irrational.

What is the Value of 9 Plus 16 Cube Root 32?

The value of ∛32 is 3.175. So, 9 + 16 × ∛32 = 9 + 16 × 3.175 = 59.8. Hence, the value of 9 plus 16 cube root 32 is 59.8.

If the Cube Root of 32 is 3.17, Find the Value of ∛0.032.

Let us represent ∛0.032 in p/q form i.e. ∛(32/1000) = 3.17/10 = 0.32. Hence, the value of ∛0.032 = 0.32.

What is the Cube Root of -32?

The cube root of -32 is equal to the negative of the cube root of 32. Therefore, ∛-32 = -(∛32) = -(3.175) = -3.175.

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