Last updated on May 26th, 2025
A number we multiply by itself three times to get the original number is its cube root. The cube root has various applications in real life, such as calculating the dimensions of cube-shaped objects and in architecture. We will now find the cube root of 485 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, ∛485 is written as 485(1/3). The cube root is the inverse operation of finding the cube of a number. For example, if ‘y’ is the cube root of 485, then y3 can be 485. Since the cube root of 485 is not an exact value, we can write it as approximately 7.82.
Finding the cube root of a number involves identifying the number that must be multiplied three times to achieve the target number. Now, we will explore different methods to find the cube root of 485. The common methods are listed below:
For a non-perfect cube like 485, we often use Halley's method.
Let's find the cube root of 485 using Halley’s method.
The formula is given by: ∛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 = 485
x = 8 (since 83 = 512 is close to 485),
∛a ≅ 8((83 + 2 × 485) / (2 × 83 + 485))
∛485 ≅ 8((512 + 970) / (1024 + 485))
∛485 ≅ 7.82
The cube root of 485 is approximately 7.82.
Finding the cube root of a number without errors can be challenging. Here are some common mistakes students make and how to avoid them:
Imagine you have a cube-shaped block with a total volume of 485 cubic centimeters. Find the length of one side of the block, equivalent to its cube root.
Side of the cube = ∛485 ≈ 7.82 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 7.82 units.
A warehouse stores 485 cubic meters of goods. Calculate the amount left after distributing 100 cubic meters.
The amount of goods left is 385 cubic meters.
To find the remaining goods, we subtract the distributed amount from the total:
485 - 100 = 385 cubic meters.
A tank holds 485 cubic meters of water. Another tank holds 150 cubic meters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 635 cubic meters.
Add the volume of both tanks:
485 + 150 = 635 cubic meters.
When the cube root of 485 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 7.82 ≈ 23.46 The cube of 23.46 ≈ 12,888.7
When we multiply the cube root of 485 by 3, it results in a significant increase in volume because the cube increases exponentially.
Find ∛(240 + 245).
∛(240 + 245) = ∛485 ≈ 7.82
As shown in the question ∛(240 + 245), we simplify by adding them.
So, 240 + 245 = 485.
Then we use this step:
∛485 ≈ 7.82 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.