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Cube Root of 197

The value of the cube root of 197 rounded to 7 decimal places is 5.8186479. It is the real solution of the equation x³ = 197. The cube root of 197 is expressed as ∛197 in the radical form and as (197)^⅓ or (197)^0.33 in the exponent form. The prime factorization of 197 is 197, hence, the cube root of 197 in its lowest radical form is expressed as ∛197.

Cube root of 197: 5.818647867
Cube root of 197 in Exponential Form: (197)^⅓
Cube root of 197 in Radical Form: ∛197

1.	What is the Cube Root of 197?
2.	How to Calculate the Cube Root of 197?
3.	Is the Cube Root of 197 Irrational?
4.	FAQs on Cube Root of 197

What is the Cube Root of 197?

The cube root of 197 is the number which when multiplied by itself three times gives the product as 197. The number 197 is prime. Therefore, the cube root of 197 = ∛197 = 5.8186.

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How to Calculate the Value of the Cube Root of 197?

Cube Root of 197 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 = 197
Let us assume x as 5
[∵ 5³ = 125 and 125 is the nearest perfect cube that is less than 197]
⇒ x = 5
Therefore,
∛197 = 5 (5³ + 2 × 197)/(2 × 5³ + 197)) = 5.81
⇒ ∛197 ≈ 5.81
Therefore, the cube root of 197 is 5.81 approximately.

Is the Cube Root of 197 Irrational?

Yes, because ∛197 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 197 is an irrational number.

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Cube Root of 197 Solved Examples

Example 1: What is the value of ∛197 ÷ ∛(-197)?

Solution:

The cube root of -197 is equal to the negative of the cube root of 197.
⇒ ∛-197 = -∛197

Therefore,
⇒ ∛197/∛(-197) = ∛197/(-∛197) = -1
Example 2: The volume of a spherical ball is 197π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 197π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 197
⇒ R = ∛(3/4 × 197) = ∛(3/4) × ∛197 = 0.90856 × 5.81865 (∵ ∛(3/4) = 0.90856 and ∛197 = 5.81865)
⇒ R = 5.28659 in³
Example 3: Given the volume of a cube is 197 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 197 in³ = a³
⇒ a³ = 197
Cube rooting on both sides,
⇒ a = ∛197 in
Since the cube root of 197 is 5.82, therefore, the length of the side of the cube is 5.82 in.

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FAQs on Cube Root of 197

What is the Value of the Cube Root of 197?

The value of the cube root of 197 is 5.81865.

If the Cube Root of 197 is 5.82, Find the Value of ∛0.197.

Let us represent ∛0.197 in p/q form i.e. ∛(197/1000) = 5.82/10 = 0.58. Hence, the value of ∛0.197 = 0.58.

Is 197 a Perfect Cube?

The number 197 is prime. Here, the prime factor 197 is not in the power of 3 and this implies that the cube root of 197 is irrational, hence 197 is not a perfect cube.

What is the Cube Root of -197?

The cube root of -197 is equal to the negative of the cube root of 197. Therefore, ∛-197 = -(∛197) = -(5.819) = -5.819.

Why is the Value of the Cube Root of 197 Irrational?

The value of the cube root of 197 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛197 is irrational.

What is the Cube of the Cube Root of 197?

The cube of the cube root of 197 is the number 197 itself i.e. (∛197)³ = (197^1/3)³ = 197.