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Cube Root of 48

The value of the cube root of 48 rounded to 5 decimal places is 3.63424. It is the real solution of the equation x³ = 48. The cube root of 48 is expressed as ∛48 or 2 ∛6 in the radical form and as (48)^⅓ or (48)^0.33 in the exponent form. The prime factorization of 48 is 2 × 2 × 2 × 2 × 3, hence, the cube root of 48 in its lowest radical form is expressed as 2 ∛6.

Cube root of 48: 3.634241186
Cube root of 48 in Exponential Form: (48)^⅓
Cube root of 48 in Radical Form: ∛48 or 2 ∛6

1.	What is the Cube Root of 48?
2.	How to Calculate the Cube Root of 48?
3.	Is the Cube Root of 48 Irrational?
4.	FAQs on Cube Root of 48

What is the Cube Root of 48?

The cube root of 48 is the number which when multiplied by itself three times gives the product as 48. Since 48 can be expressed as 2 × 2 × 2 × 2 × 3. Therefore, the cube root of 48 = ∛(2 × 2 × 2 × 2 × 3) = 3.6342.

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How to Calculate the Value of the Cube Root of 48?

Cube Root of 48 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 = 48
Let us assume x as 3
[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 48]
⇒ x = 3
Therefore,
∛48 = 3 (3³ + 2 × 48)/(2 × 3³ + 48)) = 3.62
⇒ ∛48 ≈ 3.62
Therefore, the cube root of 48 is 3.62 approximately.

Is the Cube Root of 48 Irrational?

Yes, because ∛48 = ∛(2 × 2 × 2 × 2 × 3) = 2 ∛6 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 48 is an irrational number.

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Cube Root of 48 Solved Examples

Example 1: The volume of a spherical ball is 48π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 48π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 48
⇒ R = ∛(3/4 × 48) = ∛(3/4) × ∛48 = 0.90856 × 3.63424 (∵ ∛(3/4) = 0.90856 and ∛48 = 3.63424)
⇒ R = 3.30193 in³
Example 2: What is the value of ∛48 ÷ ∛(-48)?

Solution:

The cube root of -48 is equal to the negative of the cube root of 48.
⇒ ∛-48 = -∛48

Therefore,
⇒ ∛48/∛(-48) = ∛48/(-∛48) = -1
Example 3: Given the volume of a cube is 48 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 48 in³ = a³
⇒ a³ = 48
Cube rooting on both sides,
⇒ a = ∛48 in
Since the cube root of 48 is 3.63, therefore, the length of the side of the cube is 3.63 in.

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FAQs on Cube Root of 48

What is the Value of the Cube Root of 48?

We can express 48 as 2 × 2 × 2 × 2 × 3 i.e. ∛48 = ∛(2 × 2 × 2 × 2 × 3) = 3.63424. Therefore, the value of the cube root of 48 is 3.63424.

What is the Value of 10 Plus 15 Cube Root 48?

The value of ∛48 is 3.634. So, 10 + 15 × ∛48 = 10 + 15 × 3.634 = 64.50999999999999. Hence, the value of 10 plus 15 cube root 48 is 64.50999999999999.

If the Cube Root of 48 is 3.63, Find the Value of ∛0.048.

Let us represent ∛0.048 in p/q form i.e. ∛(48/1000) = 3.63/10 = 0.36. Hence, the value of ∛0.048 = 0.36.

What is the Cube of the Cube Root of 48?

The cube of the cube root of 48 is the number 48 itself i.e. (∛48)³ = (48^1/3)³ = 48.

How to Simplify the Cube Root of 48/8?

We know that the cube root of 48 is 3.63424 and the cube root of 8 is 2. Therefore, ∛(48/8) = (∛48)/(∛8) = 3.634/2 = 1.817.

Is 48 a Perfect Cube?

The number 48 on prime factorization gives 2 × 2 × 2 × 2 × 3. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 48 is irrational, hence 48 is not a perfect cube.