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Cube Root of 17

The value of the cube root of 17 rounded to 4 decimal places is 2.5713. It is the real solution of the equation x³ = 17. The cube root of 17 is expressed as ∛17 in the radical form and as (17)^⅓ or (17)^0.33 in the exponent form. The prime factorization of 17 is 17, hence, the cube root of 17 in its lowest radical form is expressed as ∛17.

Cube root of 17: 2.571281591
Cube root of 17 in Exponential Form: (17)^⅓
Cube root of 17 in Radical Form: ∛17

1.	What is the Cube Root of 17?
2.	How to Calculate the Cube Root of 17?
3.	Is the Cube Root of 17 Irrational?
4.	FAQs on Cube Root of 17

What is the Cube Root of 17?

The cube root of 17 is the number which when multiplied by itself three times gives the product as 17. The number 17 is prime. Therefore, the cube root of 17 = ∛17 = 2.5713.

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How to Calculate the Value of the Cube Root of 17?

Cube Root of 17 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 = 17
Let us assume x as 2
[∵ 2³ = 8 and 8 is the nearest perfect cube that is less than 17]
⇒ x = 2
Therefore,
∛17 = 2 (2³ + 2 × 17)/(2 × 2³ + 17)) = 2.55
⇒ ∛17 ≈ 2.55
Therefore, the cube root of 17 is 2.55 approximately.

Is the Cube Root of 17 Irrational?

Yes, because ∛17 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 17 is an irrational number.

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Cube Root of 17 Solved Examples

Example 1: Given the volume of a cube is 17 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 17 in³ = a³
⇒ a³ = 17
Cube rooting on both sides,
⇒ a = ∛17 in
Since the cube root of 17 is 2.57, therefore, the length of the side of the cube is 2.57 in.
Example 2: What is the value of ∛17 ÷ ∛(-17)?

Solution:

The cube root of -17 is equal to the negative of the cube root of 17.
⇒ ∛-17 = -∛17

Therefore,
⇒ ∛17/∛(-17) = ∛17/(-∛17) = -1
Example 3: The volume of a spherical ball is 17π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 17π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 17
⇒ R = ∛(3/4 × 17) = ∛(3/4) × ∛17 = 0.90856 × 2.57128 (∵ ∛(3/4) = 0.90856 and ∛17 = 2.57128)
⇒ R = 2.33616 in³

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FAQs on Cube Root of 17

What is the Value of the Cube Root of 17?

The value of the cube root of 17 is 2.57128.

What is the Cube Root of -17?

The cube root of -17 is equal to the negative of the cube root of 17. Therefore, ∛-17 = -(∛17) = -(2.571) = -2.571.

If the Cube Root of 17 is 2.57, Find the Value of ∛0.017.

Let us represent ∛0.017 in p/q form i.e. ∛(17/1000) = 2.57/10 = 0.26. Hence, the value of ∛0.017 = 0.26.

What is the Cube of the Cube Root of 17?

The cube of the cube root of 17 is the number 17 itself i.e. (∛17)³ = (17^1/3)³ = 17.

How to Simplify the Cube Root of 17/64?

We know that the cube root of 17 is 2.57128 and the cube root of 64 is 4. Therefore, ∛(17/64) = (∛17)/(∛64) = 2.571/4 = 0.6428.

Why is the Value of the Cube Root of 17 Irrational?

The value of the cube root of 17 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛17 is irrational.