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Cube Root of 2401

The value of the cube root of 2401 rounded to 6 decimal places is 13.390518. It is the real solution of the equation x³ = 2401. The cube root of 2401 is expressed as ∛2401 or 7 ∛7 in the radical form and as (2401)^⅓ or (2401)^0.33 in the exponent form. The prime factorization of 2401 is 7 × 7 × 7 × 7, hence, the cube root of 2401 in its lowest radical form is expressed as 7 ∛7.

Cube root of 2401: 13.390518279
Cube root of 2401 in Exponential Form: (2401)^⅓
Cube root of 2401 in Radical Form: ∛2401 or 7 ∛7

1.	What is the Cube Root of 2401?
2.	How to Calculate the Cube Root of 2401?
3.	Is the Cube Root of 2401 Irrational?
4.	FAQs on Cube Root of 2401

What is the Cube Root of 2401?

The cube root of 2401 is the number which when multiplied by itself three times gives the product as 2401. Since 2401 can be expressed as 7 × 7 × 7 × 7. Therefore, the cube root of 2401 = ∛(7 × 7 × 7 × 7) = 13.3905.

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How to Calculate the Value of the Cube Root of 2401?

Cube Root of 2401 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 = 2401
Let us assume x as 13
[∵ 13³ = 2197 and 2197 is the nearest perfect cube that is less than 2401]
⇒ x = 13
Therefore,
∛2401 = 13 (13³ + 2 × 2401)/(2 × 13³ + 2401)) = 13.39
⇒ ∛2401 ≈ 13.39
Therefore, the cube root of 2401 is 13.39 approximately.

Is the Cube Root of 2401 Irrational?

Yes, because ∛2401 = ∛(7 × 7 × 7 × 7) = 7 ∛7 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 2401 is an irrational number.

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Cube Root of 2401 Solved Examples

Example 1: The volume of a spherical ball is 2401π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 2401π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 2401
⇒ R = ∛(3/4 × 2401) = ∛(3/4) × ∛2401 = 0.90856 × 13.39052 (∵ ∛(3/4) = 0.90856 and ∛2401 = 13.39052)
⇒ R = 12.16609 in³
Example 2: What is the value of ∛2401 ÷ ∛(-2401)?

Solution:

The cube root of -2401 is equal to the negative of the cube root of 2401.
⇒ ∛-2401 = -∛2401

Therefore,
⇒ ∛2401/∛(-2401) = ∛2401/(-∛2401) = -1
Example 3: Given the volume of a cube is 2401 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 2401 in³ = a³
⇒ a³ = 2401
Cube rooting on both sides,
⇒ a = ∛2401 in
Since the cube root of 2401 is 13.39, therefore, the length of the side of the cube is 13.39 in.

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FAQs on Cube Root of 2401

What is the Value of the Cube Root of 2401?

We can express 2401 as 7 × 7 × 7 × 7 i.e. ∛2401 = ∛(7 × 7 × 7 × 7) = 13.39052. Therefore, the value of the cube root of 2401 is 13.39052.

What is the Value of 9 Plus 10 Cube Root 2401?

The value of ∛2401 is 13.391. So, 9 + 10 × ∛2401 = 9 + 10 × 13.391 = 142.91. Hence, the value of 9 plus 10 cube root 2401 is 142.91.

If the Cube Root of 2401 is 13.39, Find the Value of ∛2.401.

Let us represent ∛2.401 in p/q form i.e. ∛(2401/1000) = 13.39/10 = 1.34. Hence, the value of ∛2.401 = 1.34.

What is the Cube Root of -2401?

The cube root of -2401 is equal to the negative of the cube root of 2401. Therefore, ∛-2401 = -(∛2401) = -(13.391) = -13.391.

Why is the Value of the Cube Root of 2401 Irrational?

The value of the cube root of 2401 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛2401 is irrational.

How to Simplify the Cube Root of 2401/729?

We know that the cube root of 2401 is 13.39052 and the cube root of 729 is 9. Therefore, ∛(2401/729) = (∛2401)/(∛729) = 13.391/9 = 1.4879.