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Cube Root of 112

The value of the cube root of 112 rounded to 5 decimal places is 4.82028. It is the real solution of the equation x³ = 112. The cube root of 112 is expressed as ∛112 or 2 ∛14 in the radical form and as (112)^⅓ or (112)^0.33 in the exponent form. The prime factorization of 112 is 2 × 2 × 2 × 2 × 7, hence, the cube root of 112 in its lowest radical form is expressed as 2 ∛14.

Cube root of 112: 4.820284528
Cube root of 112 in Exponential Form: (112)^⅓
Cube root of 112 in Radical Form: ∛112 or 2 ∛14

1.	What is the Cube Root of 112?
2.	How to Calculate the Cube Root of 112?
3.	Is the Cube Root of 112 Irrational?
4.	FAQs on Cube Root of 112

What is the Cube Root of 112?

The cube root of 112 is the number which when multiplied by itself three times gives the product as 112. Since 112 can be expressed as 2 × 2 × 2 × 2 × 7. Therefore, the cube root of 112 = ∛(2 × 2 × 2 × 2 × 7) = 4.8203.

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How to Calculate the Value of the Cube Root of 112?

Cube Root of 112 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 = 112
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 112]
⇒ x = 4
Therefore,
∛112 = 4 (4³ + 2 × 112)/(2 × 4³ + 112)) = 4.8
⇒ ∛112 ≈ 4.8
Therefore, the cube root of 112 is 4.8 approximately.

Is the Cube Root of 112 Irrational?

Yes, because ∛112 = ∛(2 × 2 × 2 × 2 × 7) = 2 ∛14 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 112 is an irrational number.

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Cube Root of 112 Solved Examples

Example 1: Given the volume of a cube is 112 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 112 in³ = a³
⇒ a³ = 112
Cube rooting on both sides,
⇒ a = ∛112 in
Since the cube root of 112 is 4.82, therefore, the length of the side of the cube is 4.82 in.
Example 2: What is the value of ∛112 ÷ ∛(-112)?

Solution:

The cube root of -112 is equal to the negative of the cube root of 112.
⇒ ∛-112 = -∛112

Therefore,
⇒ ∛112/∛(-112) = ∛112/(-∛112) = -1
Example 3: The volume of a spherical ball is 112π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 112π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 112
⇒ R = ∛(3/4 × 112) = ∛(3/4) × ∛112 = 0.90856 × 4.82028 (∵ ∛(3/4) = 0.90856 and ∛112 = 4.82028)
⇒ R = 4.37951 in³

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FAQs on Cube Root of 112

What is the Value of the Cube Root of 112?

We can express 112 as 2 × 2 × 2 × 2 × 7 i.e. ∛112 = ∛(2 × 2 × 2 × 2 × 7) = 4.82028. Therefore, the value of the cube root of 112 is 4.82028.

What is the Value of 10 Plus 14 Cube Root 112?

The value of ∛112 is 4.82. So, 10 + 14 × ∛112 = 10 + 14 × 4.82 = 77.48. Hence, the value of 10 plus 14 cube root 112 is 77.48.

Is 112 a Perfect Cube?

The number 112 on prime factorization gives 2 × 2 × 2 × 2 × 7. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 112 is irrational, hence 112 is not a perfect cube.

How to Simplify the Cube Root of 112/8?

We know that the cube root of 112 is 4.82028 and the cube root of 8 is 2. Therefore, ∛(112/8) = (∛112)/(∛8) = 4.82/2 = 2.41.

Why is the Value of the Cube Root of 112 Irrational?

The value of the cube root of 112 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛112 is irrational.

What is the Cube of the Cube Root of 112?

The cube of the cube root of 112 is the number 112 itself i.e. (∛112)³ = (112^1/3)³ = 112.