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Cube Root of 34

The value of the cube root of 34 rounded to 7 decimal places is 3.2396118. It is the real solution of the equation x³ = 34. The cube root of 34 is expressed as ∛34 in the radical form and as (34)^⅓ or (34)^0.33 in the exponent form. The prime factorization of 34 is 2 × 17, hence, the cube root of 34 in its lowest radical form is expressed as ∛34.

Cube root of 34: 3.239611801
Cube root of 34 in Exponential Form: (34)^⅓
Cube root of 34 in Radical Form: ∛34

Cube Root of 34

1.	What is the Cube Root of 34?
2.	How to Calculate the Cube Root of 34?
3.	Is the Cube Root of 34 Irrational?
4.	FAQs on Cube Root of 34

What is the Cube Root of 34?

The cube root of 34 is the number which when multiplied by itself three times gives the product as 34. Since 34 can be expressed as 2 × 17. Therefore, the cube root of 34 = ∛(2 × 17) = 3.2396.

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How to Calculate the Value of the Cube Root of 34?

Cube Root of 34 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 = 34
Let us assume x as 3
[∵ 3³ = 27 and 27 is the nearest perfect cube that is less than 34]
⇒ x = 3
Therefore,
∛34 = 3 (3³ + 2 × 34)/(2 × 3³ + 34)) = 3.24
⇒ ∛34 ≈ 3.24
Therefore, the cube root of 34 is 3.24 approximately.

Is the Cube Root of 34 Irrational?

Yes, because ∛34 = ∛(2 × 17) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 34 is an irrational number.

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Cube Root of 34 Solved Examples

Example 1: Find the real root of the equation x³ − 34 = 0.

Solution:

x³ − 34 = 0 i.e. x³ = 34
Solving for x gives us,
x = ∛34, x = ∛34 × (-1 + √3i))/2 and x = ∛34 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛34
Therefore, the real root of the equation x³ − 34 = 0 is for x = ∛34 = 3.2396.
Example 2: The volume of a spherical ball is 34π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 34π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 34
⇒ R = ∛(3/4 × 34) = ∛(3/4) × ∛34 = 0.90856 × 3.23961 (∵ ∛(3/4) = 0.90856 and ∛34 = 3.23961)
⇒ R = 2.94338 in³
Example 3: Given the volume of a cube is 34 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 34 in³ = a³
⇒ a³ = 34
Cube rooting on both sides,
⇒ a = ∛34 in
Since the cube root of 34 is 3.24, therefore, the length of the side of the cube is 3.24 in.

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FAQs on Cube Root of 34

What is the Value of the Cube Root of 34?

We can express 34 as 2 × 17 i.e. ∛34 = ∛(2 × 17) = 3.23961. Therefore, the value of the cube root of 34 is 3.23961.

What is the Value of 12 Plus 8 Cube Root 34?

The value of ∛34 is 3.24. So, 12 + 8 × ∛34 = 12 + 8 × 3.24 = 37.92. Hence, the value of 12 plus 8 cube root 34 is 37.92.

What is the Cube Root of -34?

The cube root of -34 is equal to the negative of the cube root of 34. Therefore, ∛-34 = -(∛34) = -(3.24) = -3.24.

If the Cube Root of 34 is 3.24, Find the Value of ∛0.034.

Let us represent ∛0.034 in p/q form i.e. ∛(34/1000) = 3.24/10 = 0.32. Hence, the value of ∛0.034 = 0.32.

Why is the Value of the Cube Root of 34 Irrational?

The value of the cube root of 34 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛34 is irrational.

How to Simplify the Cube Root of 34/64?

We know that the cube root of 34 is 3.23961 and the cube root of 64 is 4. Therefore, ∛(34/64) = (∛34)/(∛64) = 3.24/4 = 0.81.

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