104 LearnersLast updated on May 26th, 2025
Cube Root of 485
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.
What is the Cube Root of 485?
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 485
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:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley's method
For a non-perfect cube like 485, we often use Halley's method.
Cube Root of 485 by 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.
Common Mistakes and How to Avoid Them in the Cube Root of 485
Finding the cube root of a number without errors can be challenging. Here are some common mistakes students make and how to avoid them:
Mistake 1
Trying to find perfect cube roots for non-perfect cube numbers.
Students often try to calculate an exact whole number for the cube root of numbers like 485, which are not perfect cubes. For instance, they might assume an exact whole number exists for 485 as they do for 512. To avoid this, remember that some numbers don't have a perfect cube root; the cube root of 485 is approximately 7.82.
Mistake 2
Ignoring the exponent form
Many might overlook the fact that the cube root can also be expressed in exponent form.
For example, forgetting that the cube root of 485 is 485^(1/3). To avoid this, always learn the forms in which we can express the cube root of a number.
Mistake 3
Confusing cube root with division
Some may mistakenly assume the cube root of 485 involves dividing 485 by 3. To avoid this, remember that the cube root of 485 is the number that, when multiplied by itself three times, equals 485.
Mistake 4
Using prime factorization instead of Halley’s method
Instead of using Halley’s method for non-perfect cubes, students might use prime factorization.
For example, they might attempt to find the cube root of 485 by breaking it down into its prime factors. Remember that prime factorization can help analyze a number's factors, but it's not the best method for non-perfect cubes. Since 485 is a non-perfect cube, you can use either the approximation method or Halley’s method.
Mistake 5
Rounding too early
Rounding the cube root too early in the process can lead to errors in the subsequent steps.
For example, one might round the cube root of 485 to 7.8 too early in the calculation. To avoid this, ensure the whole calculation is done, then round the final result.
Cube Root of 485 Examples:
Problem 1
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
Explanation
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.
Problem 2
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.
Explanation
To find the remaining goods, we subtract the distributed amount from the total:
485 - 100 = 385 cubic meters.
Problem 3
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.
Explanation
Add the volume of both tanks:
485 + 150 = 635 cubic meters.
Problem 4
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
Explanation
When we multiply the cube root of 485 by 3, it results in a significant increase in volume because the cube increases exponentially.
Problem 5
Find ∛(240 + 245).
∛(240 + 245) = ∛485 ≈ 7.82
Explanation
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.
FAQs on 485 Cube Root
1.Can we find the Cube Root of 485?
2.Why is the Cube Root of 485 irrational?
3.Is it possible to get the cube root of 485 as an exact number?
4.Can we find the cube root of any number using prime factorization?
5.Is there any formula to find the cube root of a number?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Cube Root of 485?
8.How do technology and digital tools in United Kingdom support learning Algebra and Cube Root of 485?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for Cube Root of 485
- Cube root: The number that, when multiplied three times by itself, results in the given number is the cube root of that number.
- Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. A perfect cube always results in a whole number. For example, 2 × 2 × 2 = 8, therefore, 8 is a perfect cube.
- Exponent: The exponent form of the number denotes how many times a number can be multiplied by itself. In 485^(1/3), ⅓ is the exponent which denotes the cube root of 485.
- Radical sign: The symbol used to represent a root, expressed as (∛).
- Irrational number: Numbers that cannot be expressed as a simple fraction are irrational. For example, the cube root of 485 is irrational because its decimal form is non-terminating and non-repeating.
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Jaskaran Singh Saluja
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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.
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