Last updated on May 26th, 2025
A number that, when multiplied by itself three times, returns the original number is its cube root. It has various applications in real life, such as determining the dimensions of a cube-shaped container or calculating material quantities. We will now find the cube root of 582 and explain the methods used.
We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓. In exponential form, ∛582 is written as 582^(1/3). The cube root is the opposite operation of finding the cube of a number. For example, assume ‘y’ as the cube root of 582, then y^3 can be 582. Since the cube root of 582 is not an exact value, we can write it as approximately 8.331.
Finding the cube root of a number is about identifying the number that must be multiplied three times to result in the target number. Now, we will go through the different ways to find the cube root of 582. The common methods we follow to find the cube root are given below:
To find the cube root of a non-perfect cube, we often follow Halley’s method.
Since 582 is not a perfect cube, we use Halley’s method.
Let's find the cube root of 582 using Halley’s method.
The formula is ∛a ≅ x((x^3 + 2a) / (2x^3 + a)),
where:
a = the number for which the cube root is being calculated
x = the nearest perfect cube Substituting, a = 582; x = 8
∛a ≅ 8((8^3 + 2 × 582) / (2 × 8^3 + 582))
∛582 ≅ 8((512 + 1164) / (1024 + 582))
∛582 ≅ 8.331
The cube root of 582 is approximately 8.331.
Finding the cube root of a number without errors can be challenging for students. This happens for various reasons. Here are a few mistakes students commonly make and ways to avoid them:
Imagine you have a cube-shaped box that has a total volume of 582 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛582 ≈ 8.331 units
To find the side of the cube, we need to find the cube root of the given volume. Therefore, the side length of the cube is approximately 8.331 units.
A company manufactures 582 cubic meters of material. Calculate the amount of material left after using 100 cubic meters.
The amount of material left is 482 cubic meters.
To find the remaining material, subtract the used material from the total amount: 582 - 100 = 482 cubic meters.
A container holds 582 cubic meters of liquid. Another container holds a volume of 20 cubic meters. What would be the total volume if the containers are combined?
The total volume of the combined containers is 602 cubic meters.
Add the volume of both containers: 582 + 20 = 602 cubic meters.
When the cube root of 582 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 8.331 = 24.993
The cube of 24.993 ≈ 15,624.6
Multiplying the cube root of 582 by 3 results in a significant increase in volume because the cube increases exponentially.
Find ∛(250 + 332).
∛(250 + 332) = ∛582 ≈ 8.331
As shown in the question ∛(250 + 332), we can simplify that by adding them.
So, 250 + 332 = 582.
Then we use this step: ∛582 ≈ 8.331 to get the answer.
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.