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Last updated on April 4th, 2025

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Cube Root of 908

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Foundation
Intermediate
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A number we multiply by itself three times to get the original number is its cube root. It has various uses in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of 908 and explain the methods used.

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What is the Cube Root of 908?

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, ∛908 is written as 908(1/3). The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 908, then y3 can be 908. Since the cube root of 908 is not an exact value, so we can write it as approximately 9.696.

 

cube root of 908

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Finding the Cube Root of 908

Finding the cube root of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of 908. The common methods we follow to find the cube root are given below:

 

  1. Prime factorization method
  2. Approximation method
  3. Subtraction method
  4. Halley’s method

 

To find the cube root of a non-perfect number, we often follow Halley’s method. Since 908 is not a perfect cube, we use Halley’s method.

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Cube Root of 908 by Halley’s method

Let's find the cube root of 908 using Halley’s method.

 

The formula is ∛a ≅ x((x3 + 2a) / (2x3 + a))

 

where: a = the number for which the cube root is being calculated

 

x = the nearest perfect cube

 

Substituting, a = 908; x = 9

 

∛a ≅ 9((93 + 2 × 908) / (2 × 93 + 908))

 

∛908 ≅ 9((729 + 2 × 908) / (2 × 729 + 908))

 

∛908 ≅ 9.696

 

The cube root of 908 is approximately 9.696.

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Common Mistakes and How to Avoid Them in the Cube Root of 908

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Cube Root of 908 Examples:

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Problem 1

Imagine you have a cube-shaped storage box that has a total volume of 908 cubic centimeters. Find the length of one side of the box equal to its cube root.

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Explanation

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Problem 2

A warehouse has a storage space of 908 cubic meters. Calculate the amount of space left after using 108 cubic meters.

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Explanation

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Problem 3

A container holds 908 cubic meters of liquid. Another container holds a volume of 92 cubic meters. What would be the total volume if the containers are combined?

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Explanation

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Problem 4

When the cube root of 908 is multiplied by 5, calculate the resultant value. How will this affect the cube of the new value?

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Explanation

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Problem 5

Find ∛(72 + 836).

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Explanation

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FAQs on 908 Cube Root

1.Can we find the Cube Root of 908?

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2.Why is the Cube Root of 908 irrational?

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3.Is it possible to get the cube root of 908 as an exact number?

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

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

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Important Glossaries for Cube Root of 908

  • Cube root: The number that is multiplied three times by itself to get 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: 3 × 3 × 3 = 27, therefore, 27 is a perfect cube.

 

  • Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In x(1/3), ⅓ is the exponent which denotes the cube root of x.

 

  • Radical sign: The symbol that is used to represent a root, which is expressed as (∛).

 

  • Irrational number: The numbers that cannot be put in fractional forms are irrational. For example, the cube root of 908 is irrational because its decimal form goes on continuously without repeating the numbers.
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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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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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