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Cube Root of 40

The value of the cube root of 40 rounded to 6 decimal places is 3.419952. It is the real solution of the equation x³ = 40. The cube root of 40 is expressed as ∛40 or 2 ∛5 in the radical form and as (40)^⅓ or (40)^0.33 in the exponent form. The prime factorization of 40 is 2 × 2 × 2 × 5, hence, the cube root of 40 in its lowest radical form is expressed as 2 ∛5.

Cube root of 40: 3.419951893
Cube root of 40 in Exponential Form: (40)^⅓
Cube root of 40 in Radical Form: ∛40 or 2 ∛5

Cube Root of 40

1.	What is the Cube Root of 40?
2.	How to Calculate the Cube Root of 40?
3.	Is the Cube Root of 40 Irrational?
4.	FAQs on Cube Root of 40

What is the Cube Root of 40?

The cube root of 40 is the number which when multiplied by itself three times gives the product as 40. Since 40 can be expressed as 2 × 2 × 2 × 5. Therefore, the cube root of 40 = ∛(2 × 2 × 2 × 5) = 3.42.

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How to Calculate the Value of the Cube Root of 40?

Cube Root of 40 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 = 40
Let us assume x as 3
[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 40]
⇒ x = 3
Therefore,
∛40 = 3 (3³ + 2 × 40)/(2 × 3³ + 40)) = 3.41
⇒ ∛40 ≈ 3.41
Therefore, the cube root of 40 is 3.41 approximately.

Is the Cube Root of 40 Irrational?

Yes, because ∛40 = ∛(2 × 2 × 2 × 5) = 2 ∛5 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 40 is an irrational number.

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Cube Root of 40 Solved Examples

Example 1: Find the real root of the equation x³ − 40 = 0.

Solution:

x³ − 40 = 0 i.e. x³ = 40
Solving for x gives us,
x = ∛40, x = ∛40 × (-1 + √3i))/2 and x = ∛40 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛40
Therefore, the real root of the equation x³ − 40 = 0 is for x = ∛40 = 3.42.
Example 2: The volume of a spherical ball is 40π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 40π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 40
⇒ R = ∛(3/4 × 40) = ∛(3/4) × ∛40 = 0.90856 × 3.41995 (∵ ∛(3/4) = 0.90856 and ∛40 = 3.41995)
⇒ R = 3.10723 in³
Example 3: What is the value of ∛40 ÷ ∛(-40)?

Solution:

The cube root of -40 is equal to the negative of the cube root of 40.
⇒ ∛-40 = -∛40

Therefore,
⇒ ∛40/∛(-40) = ∛40/(-∛40) = -1

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FAQs on Cube Root of 40

What is the Value of the Cube Root of 40?

We can express 40 as 2 × 2 × 2 × 5 i.e. ∛40 = ∛(2 × 2 × 2 × 5) = 3.41995. Therefore, the value of the cube root of 40 is 3.41995.

What is the Cube of the Cube Root of 40?

The cube of the cube root of 40 is the number 40 itself i.e. (∛40)³ = (40^1/3)³ = 40.

What is the Cube Root of -40?

The cube root of -40 is equal to the negative of the cube root of 40. Therefore, ∛-40 = -(∛40) = -(3.42) = -3.42.

Why is the Value of the Cube Root of 40 Irrational?

The value of the cube root of 40 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛40 is irrational.

How to Simplify the Cube Root of 40/64?

We know that the cube root of 40 is 3.41995 and the cube root of 64 is 4. Therefore, ∛(40/64) = (∛40)/(∛64) = 3.42/4 = 0.855.

If the Cube Root of 40 is 3.42, Find the Value of ∛0.04.

Let us represent ∛0.04 in p/q form i.e. ∛(40/1000) = 3.42/10 = 0.34. Hence, the value of ∛0.04 = 0.34.

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