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Cube Root of 91

The value of the cube root of 91 rounded to 6 decimal places is 4.497941. It is the real solution of the equation x³ = 91. The cube root of 91 is expressed as ∛91 in the radical form and as (91)^⅓ or (91)^0.33 in the exponent form. The prime factorization of 91 is 7 × 13, hence, the cube root of 91 in its lowest radical form is expressed as ∛91.

Cube root of 91: 4.497941445
Cube root of 91 in Exponential Form: (91)^⅓
Cube root of 91 in Radical Form: ∛91

Cube Root of 91

1.	What is the Cube Root of 91?
2.	How to Calculate the Cube Root of 91?
3.	Is the Cube Root of 91 Irrational?
4.	FAQs on Cube Root of 91

What is the Cube Root of 91?

The cube root of 91 is the number which when multiplied by itself three times gives the product as 91. Since 91 can be expressed as 7 × 13. Therefore, the cube root of 91 = ∛(7 × 13) = 4.4979.

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How to Calculate the Value of the Cube Root of 91?

Cube Root of 91 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 = 91
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 91]
⇒ x = 4
Therefore,
∛91 = 4 (4³ + 2 × 91)/(2 × 4³ + 91)) = 4.49
⇒ ∛91 ≈ 4.49
Therefore, the cube root of 91 is 4.49 approximately.

Is the Cube Root of 91 Irrational?

Yes, because ∛91 = ∛(7 × 13) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 91 is an irrational number.

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Cube Root of 91 Solved Examples

Example 1: Given the volume of a cube is 91 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 91 in³ = a³
⇒ a³ = 91
Cube rooting on both sides,
⇒ a = ∛91 in
Since the cube root of 91 is 4.5, therefore, the length of the side of the cube is 4.5 in.
Example 2: The volume of a spherical ball is 91π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 91π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 91
⇒ R = ∛(3/4 × 91) = ∛(3/4) × ∛91 = 0.90856 × 4.49794 (∵ ∛(3/4) = 0.90856 and ∛91 = 4.49794)
⇒ R = 4.08665 in³
Example 3: Find the real root of the equation x³ − 91 = 0.

Solution:

x³ − 91 = 0 i.e. x³ = 91
Solving for x gives us,
x = ∛91, x = ∛91 × (-1 + √3i))/2 and x = ∛91 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛91
Therefore, the real root of the equation x³ − 91 = 0 is for x = ∛91 = 4.4979.

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FAQs on Cube Root of 91

What is the Value of the Cube Root of 91?

We can express 91 as 7 × 13 i.e. ∛91 = ∛(7 × 13) = 4.49794. Therefore, the value of the cube root of 91 is 4.49794.

Is 91 a Perfect Cube?

The number 91 on prime factorization gives 7 × 13. Here, the prime factor 7 is not in the power of 3. Therefore the cube root of 91 is irrational, hence 91 is not a perfect cube.

What is the Cube Root of -91?

The cube root of -91 is equal to the negative of the cube root of 91. Therefore, ∛-91 = -(∛91) = -(4.498) = -4.498.

What is the Value of 14 Plus 7 Cube Root 91?

The value of ∛91 is 4.498. So, 14 + 7 × ∛91 = 14 + 7 × 4.498 = 45.486000000000004. Hence, the value of 14 plus 7 cube root 91 is 45.486000000000004.

What is the Cube of the Cube Root of 91?

The cube of the cube root of 91 is the number 91 itself i.e. (∛91)³ = (91^1/3)³ = 91.

If the Cube Root of 91 is 4.5, Find the Value of ∛0.091.

Let us represent ∛0.091 in p/q form i.e. ∛(91/1000) = 4.5/10 = 0.45. Hence, the value of ∛0.091 = 0.45.

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