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Cube Root of 68

The value of the cube root of 68 rounded to 5 decimal places is 4.08166. It is the real solution of the equation x³ = 68. The cube root of 68 is expressed as ∛68 in the radical form and as (68)^⅓ or (68)^0.33 in the exponent form. The prime factorization of 68 is 2 × 2 × 17, hence, the cube root of 68 in its lowest radical form is expressed as ∛68.

Cube root of 68: 4.081655102
Cube root of 68 in Exponential Form: (68)^⅓
Cube root of 68 in Radical Form: ∛68

Cube Root of 68

1.	What is the Cube Root of 68?
2.	How to Calculate the Cube Root of 68?
3.	Is the Cube Root of 68 Irrational?
4.	FAQs on Cube Root of 68

What is the Cube Root of 68?

The cube root of 68 is the number which when multiplied by itself three times gives the product as 68. Since 68 can be expressed as 2 × 2 × 17. Therefore, the cube root of 68 = ∛(2 × 2 × 17) = 4.0817.

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How to Calculate the Value of the Cube Root of 68?

Cube Root of 68 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 = 68
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 68]
⇒ x = 4
Therefore,
∛68 = 4 (4³ + 2 × 68)/(2 × 4³ + 68)) = 4.08
⇒ ∛68 ≈ 4.08
Therefore, the cube root of 68 is 4.08 approximately.

Is the Cube Root of 68 Irrational?

Yes, because ∛68 = ∛(2 × 2 × 17) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 68 is an irrational number.

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Cube Root of 68 Solved Examples

Example 1: What is the value of ∛68 + ∛(-68)?

Solution:

The cube root of -68 is equal to the negative of the cube root of 68.
i.e. ∛-68 = -∛68

Therefore, ∛68 + ∛(-68) = ∛68 - ∛68 = 0
Example 2: Find the real root of the equation x³ − 68 = 0.

Solution:

x³ − 68 = 0 i.e. x³ = 68
Solving for x gives us,
x = ∛68, x = ∛68 × (-1 + √3i))/2 and x = ∛68 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛68
Therefore, the real root of the equation x³ − 68 = 0 is for x = ∛68 = 4.0817.
Example 3: Given the volume of a cube is 68 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 68 in³ = a³
⇒ a³ = 68
Cube rooting on both sides,
⇒ a = ∛68 in
Since the cube root of 68 is 4.08, therefore, the length of the side of the cube is 4.08 in.

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FAQs on Cube Root of 68

What is the Value of the Cube Root of 68?

We can express 68 as 2 × 2 × 17 i.e. ∛68 = ∛(2 × 2 × 17) = 4.08166. Therefore, the value of the cube root of 68 is 4.08166.

What is the Cube Root of -68?

The cube root of -68 is equal to the negative of the cube root of 68. Therefore, ∛-68 = -(∛68) = -(4.082) = -4.082.

Is 68 a Perfect Cube?

The number 68 on prime factorization gives 2 × 2 × 17. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 68 is irrational, hence 68 is not a perfect cube.

What is the Value of 13 Plus 17 Cube Root 68?

The value of ∛68 is 4.082. So, 13 + 17 × ∛68 = 13 + 17 × 4.082 = 82.39399999999999. Hence, the value of 13 plus 17 cube root 68 is 82.39399999999999.

If the Cube Root of 68 is 4.08, Find the Value of ∛0.068.

Let us represent ∛0.068 in p/q form i.e. ∛(68/1000) = 4.08/10 = 0.41. Hence, the value of ∛0.068 = 0.41.

What is the Cube of the Cube Root of 68?

The cube of the cube root of 68 is the number 68 itself i.e. (∛68)³ = (68^1/3)³ = 68.

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