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Cube Root of 196

The value of the cube root of 196 rounded to 5 decimal places is 5.80879. It is the real solution of the equation x³ = 196. The cube root of 196 is expressed as ∛196 in the radical form and as (196)^⅓ or (196)^0.33 in the exponent form. The prime factorization of 196 is 2 × 2 × 7 × 7, hence, the cube root of 196 in its lowest radical form is expressed as ∛196.

Cube root of 196: 5.808785734
Cube root of 196 in Exponential Form: (196)^⅓
Cube root of 196 in Radical Form: ∛196

Cube Root of 196

1.	What is the Cube Root of 196?
2.	How to Calculate the Cube Root of 196?
3.	Is the Cube Root of 196 Irrational?
4.	FAQs on Cube Root of 196

What is the Cube Root of 196?

The cube root of 196 is the number which when multiplied by itself three times gives the product as 196. Since 196 can be expressed as 2 × 2 × 7 × 7. Therefore, the cube root of 196 = ∛(2 × 2 × 7 × 7) = 5.8088.

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How to Calculate the Value of the Cube Root of 196?

Cube Root of 196 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 = 196
Let us assume x as 5
[∵ 5³ = 125 and 125 is the nearest perfect cube that is less than 196]
⇒ x = 5
Therefore,
∛196 = 5 (5³ + 2 × 196)/(2 × 5³ + 196)) = 5.8
⇒ ∛196 ≈ 5.8
Therefore, the cube root of 196 is 5.8 approximately.

Is the Cube Root of 196 Irrational?

Yes, because ∛196 = ∛(2 × 2 × 7 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 196 is an irrational number.

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Cube Root of 196 Solved Examples

Example 1: The volume of a spherical ball is 196π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 196π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 196
⇒ R = ∛(3/4 × 196) = ∛(3/4) × ∛196 = 0.90856 × 5.80879 (∵ ∛(3/4) = 0.90856 and ∛196 = 5.80879)
⇒ R = 5.27763 in³
Example 2: What is the value of ∛196 + ∛(-196)?

Solution:

The cube root of -196 is equal to the negative of the cube root of 196.
i.e. ∛-196 = -∛196

Therefore, ∛196 + ∛(-196) = ∛196 - ∛196 = 0
Example 3: Find the real root of the equation x³ − 196 = 0.

Solution:

x³ − 196 = 0 i.e. x³ = 196
Solving for x gives us,
x = ∛196, x = ∛196 × (-1 + √3i))/2 and x = ∛196 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛196
Therefore, the real root of the equation x³ − 196 = 0 is for x = ∛196 = 5.8088.

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FAQs on Cube Root of 196

What is the Value of the Cube Root of 196?

We can express 196 as 2 × 2 × 7 × 7 i.e. ∛196 = ∛(2 × 2 × 7 × 7) = 5.80879. Therefore, the value of the cube root of 196 is 5.80879.

If the Cube Root of 196 is 5.81, Find the Value of ∛0.196.

Let us represent ∛0.196 in p/q form i.e. ∛(196/1000) = 5.81/10 = 0.58. Hence, the value of ∛0.196 = 0.58.

How to Simplify the Cube Root of 196/8?

We know that the cube root of 196 is 5.80879 and the cube root of 8 is 2. Therefore, ∛(196/8) = (∛196)/(∛8) = 5.809/2 = 2.9045.

What is the Cube Root of -196?

The cube root of -196 is equal to the negative of the cube root of 196. Therefore, ∛-196 = -(∛196) = -(5.809) = -5.809.

Is 196 a Perfect Cube?

The number 196 on prime factorization gives 2 × 2 × 7 × 7. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 196 is irrational, hence 196 is not a perfect cube.

What is the Cube of the Cube Root of 196?

The cube of the cube root of 196 is the number 196 itself i.e. (∛196)³ = (196^1/3)³ = 196.

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