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Cube Root of 4096

The value of the cube root of 4096 is 16. It is the real solution of the equation x³ = 4096. The cube root of 4096 is expressed as ∛4096 in radical form and as (4096)^⅓ or (4096)^0.33 in the exponent form. As the cube root of 4096 is a whole number, 4096 is a perfect cube.

Cube root of 4096: 16
Cube root of 4096 in exponential form: (4096)^⅓
Cube root of 4096 in radical form: ∛4096

Cube Root of 4096

1.	What is the Cube Root of 4096?
2.	How to Calculate the Cube Root of 4096?
3.	Is the Cube Root of 4096 Irrational?
4.	FAQs on Cube Root of 4096

What is the Cube Root of 4096?

The cube root of 4096 is the number which when multiplied by itself three times gives the product as 4096. Since 4096 can be expressed as 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Therefore, the cube root of 4096 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2) = 16.

How to Calculate the Value of the Cube Root of 4096?

Cube Root of 4096 by Prime Factorization

Prime factorization of 4096 is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Simplifying the above expression: 2¹²
Simplifying further: 16³

Therefore, the cube root of 4096 by prime factorization is (2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2)^1/3 = 16.

Is the Cube Root of 4096 Irrational?

No, because ∛4096 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2) can be expressed in the form of p/q i.e. 16/1. Therefore, the value of the cube root of 4096 is an integer (rational).

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Cube Root of 4096 Solved Examples

Example 1: What is the value of ∛4096 + ∛(-4096)?

Solution:

The cube root of -4096 is equal to the negative of the cube root of 4096.
i.e. ∛-4096 = -∛4096

Therefore, ∛4096 + ∛(-4096) = ∛4096 - ∛4096 = 0
Example 2: Given the volume of a cube is 4096 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 4096 in³ = a³
⇒ a³ = 4096
Cube rooting on both sides,
⇒ a = ∛4096 in
Since the cube root of 4096 is 16, therefore, the length of the side of the cube is 16 in.
Example 3: The volume of a spherical ball is 4096π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 4096π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 4096
⇒ R = ∛(3/4 × 4096) = ∛(3/4) × ∛4096 = 0.90856 × 16 (∵ ∛(3/4) = 0.90856 and ∛4096 = 16)
⇒ R = 14.53696 in³

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FAQs on Cube Root of 4096

What is the Value of the Cube Root of 4096?

We can express 4096 as 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 i.e. ∛4096 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2) = 16. Therefore, the value of the cube root of 4096 is 16.

What is the Value of 11 Plus 8 Cube Root 4096?

The value of ∛4096 is 16. So, 11 + 8 × ∛4096 = 11 + 8 × 16 = 139. Hence, the value of 11 plus 8 cube root 4096 is 139.

Is 4096 a Perfect Cube?

The number 4096 on prime factorization gives 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. On combining the prime factors in groups of 3 gives 16. So, the cube root of 4096 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2) = 16 (perfect cube).

What is the Cube Root of -4096?

The cube root of -4096 is equal to the negative of the cube root of 4096. Therefore, ∛-4096 = -(∛4096) = -(16) = -16.

What is the Cube of the Cube Root of 4096?

The cube of the cube root of 4096 is the number 4096 itself i.e. (∛4096)³ = (4096^1/3)³ = 4096.

Why is the value of the Cube Root of 4096 Rational?

The value of the cube root of 4096 can be expressed in the form of p/q i.e. = 16/1, where q ≠ 0. Therefore, the ∛4096 is rational.

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