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Cube Root of 1331

The value of the cube root of 1331 is 11. It is the real solution of the equation x³ = 1331. The cube root of 1331 is expressed as ∛1331 in radical form and as (1331)^⅓ or (1331)^0.33 in the exponent form. As the cube root of 1331 is a whole number, 1331 is a perfect cube.

Cube root of 1331: 11
Cube root of 1331 in exponential form: (1331)^⅓
Cube root of 1331 in radical form: ∛1331

Cube Root of 1331

1.	What is the Cube Root of 1331?
2.	How to Calculate the Cube Root of 1331?
3.	Is the Cube Root of 1331 Irrational?
4.	FAQs on Cube Root of 1331

What is the Cube Root of 1331?

The cube root of 1331 is the number which when multiplied by itself three times gives the product as 1331. Since 1331 can be expressed as 11 × 11 × 11. Therefore, the cube root of 1331 = ∛(11 × 11 × 11) = 11.

How to Calculate the Value of the Cube Root of 1331?

Cube Root of 1331 by Prime Factorization

Prime factorization of 1331 is 11 × 11 × 11
Simplifying the above expression: 11³

Therefore, the cube root of 1331 by prime factorization is (11 × 11 × 11)^1/3 = 11.

Is the Cube Root of 1331 Irrational?

No, because ∛1331 = ∛(11 × 11 × 11) can be expressed in the form of p/q i.e. 11/1. Therefore, the value of the cube root of 1331 is an integer (rational).

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Cube Root of 1331 Solved Examples

Example 1: The volume of a spherical ball is 1331π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 1331π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 1331
⇒ R = ∛(3/4 × 1331) = ∛(3/4) × ∛1331 = 0.90856 × 11 (∵ ∛(3/4) = 0.90856 and ∛1331 = 11)
⇒ R = 9.99416 in³
Example 2: What is the value of ∛1331 ÷ ∛(-1331)?

Solution:

The cube root of -1331 is equal to the negative of the cube root of 1331.
⇒ ∛-1331 = -∛1331

Therefore,
⇒ ∛1331/∛(-1331) = ∛1331/(-∛1331) = -1
Example 3: Find the real root of the equation x³ − 1331 = 0.

Solution:

x³ − 1331 = 0 i.e. x³ = 1331
Solving for x gives us,
x = ∛1331, x = ∛1331 × (-1 + √3i))/2 and x = ∛1331 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛1331
Therefore, the real root of the equation x³ − 1331 = 0 is for x = ∛1331 = 11.

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FAQs on Cube Root of 1331

What is the Value of the Cube Root of 1331?

We can express 1331 as 11 × 11 × 11 i.e. ∛1331 = ∛(11 × 11 × 11) = 11. Therefore, the value of the cube root of 1331 is 11.

What is the Cube Root of -1331?

The cube root of -1331 is equal to the negative of the cube root of 1331. Therefore, ∛-1331 = -(∛1331) = -(11) = -11.

If the Cube Root of 1331 is 11, Find the Value of ∛1.331.

Let us represent ∛1.331 in p/q form i.e. ∛(1331/1000) = 11/10 = 1.1. Hence, the value of ∛1.331 = 1.1.

What is the Cube of the Cube Root of 1331?

The cube of the cube root of 1331 is the number 1331 itself i.e. (∛1331)³ = (1331^1/3)³ = 1331.

Why is the value of the Cube Root of 1331 Rational?

The value of the cube root of 1331 can be expressed in the form of p/q i.e. = 11/1, where q ≠ 0. Therefore, the ∛1331 is rational.

What is the Value of 16 Plus 11 Cube Root 1331?

The value of ∛1331 is 11. So, 16 + 11 × ∛1331 = 16 + 11 × 11 = 137. Hence, the value of 16 plus 11 cube root 1331 is 137.

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