Cube Root of 485
2026-02-28 17:44 Diff
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Last updated on August 5, 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.

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.

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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:

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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.

Okay, lets begin

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.

Well explained 👍

Problem 2

A warehouse stores 485 cubic meters of goods. Calculate the amount left after distributing 100 cubic meters.

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

The total volume of the combined tanks is 635 cubic meters.

Explanation

Add the volume of both tanks:

485 + 150 = 635 cubic meters.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find ∛(240 + 245).

Okay, lets begin

∛(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.

Well explained 👍

FAQs on 485 Cube Root

1.Can we find the Cube Root of 485?

No, we cannot find the cube root of 485 exactly as a whole number. It is approximately 7.82.

2.Why is the Cube Root of 485 irrational?

The cube root of 485 is irrational because its decimal value is non-terminating and non-repeating.

3.Is it possible to get the cube root of 485 as an exact number?

No, the cube root of 485 is not an exact whole number. It is a decimal that is about 7.82.

4.Can we find the cube root of any number using prime factorization?

The prime factorization method can be used to calculate the cube root of perfect cube numbers, but it is not suitable for non-perfect cubes. For example, 2 × 2 × 2 = 8, so 8 is a perfect cube.

5.Is there any formula to find the cube root of a number?

Yes, the formula we use for the cube root of any number ‘a’ using Halley's method is ∛a ≅ x((x^3 + 2a) / (2x^3 + a)).

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

About the Author

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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