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 x^{3} = 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
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.
☛ Check: Cube Root Calculator
How to Calculate the Value of the Cube Root of 196?
Cube Root of 196 by Halley's Method
Its formula is ∛a ≈ x ((x^{3} + 2a)/(2x^{3} + 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
[∵ 5^{3} = 125 and 125 is the nearest perfect cube that is less than 196]
⇒ x = 5
Therefore,
∛196 = 5 (5^{3} + 2 × 196)/(2 × 5^{3} + 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.
☛ Also Check:
 Cube Root of 400
 Cube Root of 1024
 Cube Root of 100
 Cube Root of 42
 Cube Root of 14
 Cube Root of 108
 Cube Root of 144
Cube Root of 196 Solved Examples

Example 1: The volume of a spherical ball is 196π in^{3}. What is the radius of this ball?
Solution:
Volume of the spherical ball = 196π in^{3}
= 4/3 × π × R^{3}
⇒ R^{3} = 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 in^{3} 
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 x^{3} − 196 = 0.
Solution:
x^{3} − 196 = 0 i.e. x^{3} = 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 x^{3} − 196 = 0 is for x = ∛196 = 5.8088.
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.