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Cube Root of 1024

The value of the cube root of 1024 rounded to 6 decimal places is 10.079368. It is the real solution of the equation x³ = 1024. The cube root of 1024 is expressed as ∛1024 or 8 ∛2 in the radical form and as (1024)^⅓ or (1024)^0.33 in the exponent form. The prime factorization of 1024 is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2, hence, the cube root of 1024 in its lowest radical form is expressed as 8 ∛2.

Cube root of 1024: 10.079368399
Cube root of 1024 in Exponential Form: (1024)^⅓
Cube root of 1024 in Radical Form: ∛1024 or 8 ∛2

Cube Root of 1024

1.	What is the Cube Root of 1024?
2.	How to Calculate the Cube Root of 1024?
3.	Is the Cube Root of 1024 Irrational?
4.	FAQs on Cube Root of 1024

What is the Cube Root of 1024?

The cube root of 1024 is the number which when multiplied by itself three times gives the product as 1024. Since 1024 can be expressed as 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Therefore, the cube root of 1024 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2) = 10.0794.

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How to Calculate the Value of the Cube Root of 1024?

Cube Root of 1024 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 = 1024
Let us assume x as 10
[∵ 10³ = 1000 and 1000 is the nearest perfect cube that is less than 1024]
⇒ x = 10
Therefore,
∛1024 = 10 (10³ + 2 × 1024)/(2 × 10³ + 1024)) = 10.08
⇒ ∛1024 ≈ 10.08
Therefore, the cube root of 1024 is 10.08 approximately.

Is the Cube Root of 1024 Irrational?

Yes, because ∛1024 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2) = 8 ∛2 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 1024 is an irrational number.

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Cube Root of 1024 Solved Examples

Example 1: Find the real root of the equation x³ − 1024 = 0.

Solution:

x³ − 1024 = 0 i.e. x³ = 1024
Solving for x gives us,
x = ∛1024, x = ∛1024 × (-1 + √3i))/2 and x = ∛1024 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛1024
Therefore, the real root of the equation x³ − 1024 = 0 is for x = ∛1024 = 10.0794.
Example 2: Given the volume of a cube is 1024 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 1024 in³ = a³
⇒ a³ = 1024
Cube rooting on both sides,
⇒ a = ∛1024 in
Since the cube root of 1024 is 10.08, therefore, the length of the side of the cube is 10.08 in.
Example 3: The volume of a spherical ball is 1024π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 1024π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 1024
⇒ R = ∛(3/4 × 1024) = ∛(3/4) × ∛1024 = 0.90856 × 10.07937 (∵ ∛(3/4) = 0.90856 and ∛1024 = 10.07937)
⇒ R = 9.15771 in³

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FAQs on Cube Root of 1024

What is the Value of the Cube Root of 1024?

We can express 1024 as 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 i.e. ∛1024 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2) = 10.07937. Therefore, the value of the cube root of 1024 is 10.07937.

Why is the Value of the Cube Root of 1024 Irrational?

The value of the cube root of 1024 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛1024 is irrational.

How to Simplify the Cube Root of 1024/512?

We know that the cube root of 1024 is 10.07937 and the cube root of 512 is 8. Therefore, ∛(1024/512) = (∛1024)/(∛512) = 10.079/8 = 1.2599.

If the Cube Root of 1024 is 10.08, Find the Value of ∛1.024.

Let us represent ∛1.024 in p/q form i.e. ∛(1024/1000) = 10.08/10 = 1.01. Hence, the value of ∛1.024 = 1.01.

What is the Cube Root of -1024?

The cube root of -1024 is equal to the negative of the cube root of 1024. Therefore, ∛-1024 = -(∛1024) = -(10.079) = -10.079.

What is the Value of 13 Plus 12 Cube Root 1024?

The value of ∛1024 is 10.079. So, 13 + 12 × ∛1024 = 13 + 12 × 10.079 = 133.948. Hence, the value of 13 plus 12 cube root 1024 is 133.948.

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