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Cube Root of 126

The value of the cube root of 126 rounded to 4 decimal places is 5.0133. It is the real solution of the equation x³ = 126. The cube root of 126 is expressed as ∛126 in the radical form and as (126)^⅓ or (126)^0.33 in the exponent form. The prime factorization of 126 is 2 × 3 × 3 × 7, hence, the cube root of 126 in its lowest radical form is expressed as ∛126.

Cube root of 126: 5.013297935
Cube root of 126 in Exponential Form: (126)^⅓
Cube root of 126 in Radical Form: ∛126

Cube Root of 126

1.	What is the Cube Root of 126?
2.	How to Calculate the Cube Root of 126?
3.	Is the Cube Root of 126 Irrational?
4.	FAQs on Cube Root of 126

What is the Cube Root of 126?

The cube root of 126 is the number which when multiplied by itself three times gives the product as 126. Since 126 can be expressed as 2 × 3 × 3 × 7. Therefore, the cube root of 126 = ∛(2 × 3 × 3 × 7) = 5.0133.

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How to Calculate the Value of the Cube Root of 126?

Cube Root of 126 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 = 126
Let us assume x as 5
[∵ 5³ = 125 and 125 is the nearest perfect cube that is less than 126]
⇒ x = 5
Therefore,
∛126 = 5 (5³ + 2 × 126)/(2 × 5³ + 126)) = 5.01
⇒ ∛126 ≈ 5.01
Therefore, the cube root of 126 is 5.01 approximately.

Is the Cube Root of 126 Irrational?

Yes, because ∛126 = ∛(2 × 3 × 3 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 126 is an irrational number.

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Cube Root of 126 Solved Examples

Example 1: Find the real root of the equation x³ − 126 = 0.

Solution:

x³ − 126 = 0 i.e. x³ = 126
Solving for x gives us,
x = ∛126, x = ∛126 × (-1 + √3i))/2 and x = ∛126 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛126
Therefore, the real root of the equation x³ − 126 = 0 is for x = ∛126 = 5.0133.
Example 2: The volume of a spherical ball is 126π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 126π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 126
⇒ R = ∛(3/4 × 126) = ∛(3/4) × ∛126 = 0.90856 × 5.0133 (∵ ∛(3/4) = 0.90856 and ∛126 = 5.0133)
⇒ R = 4.55488 in³
Example 3: Given the volume of a cube is 126 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 126 in³ = a³
⇒ a³ = 126
Cube rooting on both sides,
⇒ a = ∛126 in
Since the cube root of 126 is 5.01, therefore, the length of the side of the cube is 5.01 in.

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FAQs on Cube Root of 126

What is the Value of the Cube Root of 126?

We can express 126 as 2 × 3 × 3 × 7 i.e. ∛126 = ∛(2 × 3 × 3 × 7) = 5.0133. Therefore, the value of the cube root of 126 is 5.0133.

What is the Value of 16 Plus 13 Cube Root 126?

The value of ∛126 is 5.013. So, 16 + 13 × ∛126 = 16 + 13 × 5.013 = 81.169. Hence, the value of 16 plus 13 cube root 126 is 81.169.

If the Cube Root of 126 is 5.01, Find the Value of ∛0.126.

Let us represent ∛0.126 in p/q form i.e. ∛(126/1000) = 5.01/10 = 0.5. Hence, the value of ∛0.126 = 0.5.

What is the Cube of the Cube Root of 126?

The cube of the cube root of 126 is the number 126 itself i.e. (∛126)³ = (126^1/3)³ = 126.

Why is the Value of the Cube Root of 126 Irrational?

The value of the cube root of 126 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛126 is irrational.

Is 126 a Perfect Cube?

The number 126 on prime factorization gives 2 × 3 × 3 × 7. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 126 is irrational, hence 126 is not a perfect cube.

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