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Cube Root of 140

The value of the cube root of 140 rounded to 4 decimal places is 5.1925. It is the real solution of the equation x³ = 140. The cube root of 140 is expressed as ∛140 in the radical form and as (140)^⅓ or (140)^0.33 in the exponent form. The prime factorization of 140 is 2 × 2 × 5 × 7, hence, the cube root of 140 in its lowest radical form is expressed as ∛140.

Cube root of 140: 5.192494102
Cube root of 140 in Exponential Form: (140)^⅓
Cube root of 140 in Radical Form: ∛140

1.	What is the Cube Root of 140?
2.	How to Calculate the Cube Root of 140?
3.	Is the Cube Root of 140 Irrational?
4.	FAQs on Cube Root of 140

What is the Cube Root of 140?

The cube root of 140 is the number which when multiplied by itself three times gives the product as 140. Since 140 can be expressed as 2 × 2 × 5 × 7. Therefore, the cube root of 140 = ∛(2 × 2 × 5 × 7) = 5.1925.

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How to Calculate the Value of the Cube Root of 140?

Cube Root of 140 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 = 140
Let us assume x as 5
[∵ 5³ = 125 and 125 is the nearest perfect cube that is less than 140]
⇒ x = 5
Therefore,
∛140 = 5 (5³ + 2 × 140)/(2 × 5³ + 140)) = 5.19
⇒ ∛140 ≈ 5.19
Therefore, the cube root of 140 is 5.19 approximately.

Is the Cube Root of 140 Irrational?

Yes, because ∛140 = ∛(2 × 2 × 5 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 140 is an irrational number.

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Cube Root of 140 Solved Examples

Example 1: What is the value of ∛140 + ∛(-140)?

Solution:

The cube root of -140 is equal to the negative of the cube root of 140.
i.e. ∛-140 = -∛140

Therefore, ∛140 + ∛(-140) = ∛140 - ∛140 = 0
Example 2: Given the volume of a cube is 140 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 140 in³ = a³
⇒ a³ = 140
Cube rooting on both sides,
⇒ a = ∛140 in
Since the cube root of 140 is 5.19, therefore, the length of the side of the cube is 5.19 in.
Example 3: The volume of a spherical ball is 140π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 140π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 140
⇒ R = ∛(3/4 × 140) = ∛(3/4) × ∛140 = 0.90856 × 5.19249 (∵ ∛(3/4) = 0.90856 and ∛140 = 5.19249)
⇒ R = 4.71769 in³

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FAQs on Cube Root of 140

What is the Value of the Cube Root of 140?

We can express 140 as 2 × 2 × 5 × 7 i.e. ∛140 = ∛(2 × 2 × 5 × 7) = 5.19249. Therefore, the value of the cube root of 140 is 5.19249.

What is the Cube Root of -140?

The cube root of -140 is equal to the negative of the cube root of 140. Therefore, ∛-140 = -(∛140) = -(5.192) = -5.192.

What is the Value of 16 Plus 7 Cube Root 140?

The value of ∛140 is 5.192. So, 16 + 7 × ∛140 = 16 + 7 × 5.192 = 52.344. Hence, the value of 16 plus 7 cube root 140 is 52.344.

Why is the Value of the Cube Root of 140 Irrational?

The value of the cube root of 140 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛140 is irrational.

If the Cube Root of 140 is 5.19, Find the Value of ∛0.14.

Let us represent ∛0.14 in p/q form i.e. ∛(140/1000) = 5.19/10 = 0.52. Hence, the value of ∛0.14 = 0.52.

What is the Cube of the Cube Root of 140?

The cube of the cube root of 140 is the number 140 itself i.e. (∛140)³ = (140^1/3)³ = 140.