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Last updated on April 28th, 2025

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Cube Root of 117649

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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 117649 and explain the methods used.

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What is the Cube Root of 117649?

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, ∛117649 is written as 117649(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 117649, then y³ can be 117649. Since 117649 is a perfect cube, its cube root is exactly 49.

cube root of 117649

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Finding the Cube Root of 117649

Finding the cube root of a number involves identifying the number that, when multiplied three times by itself, results in the target number. Now, we will go through the different ways to find the cube root of 117649. The common methods we follow to find the cube root are given below:

 

  • Prime factorization method
  • Approximation method
  • Subtraction method
  • Halley’s method

 

Since 117649 is a perfect cube, we can use the prime factorization method efficiently.

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Cube Root of 117649 by Prime Factorization Method

Let's find the cube root of 117649 using the prime factorization method.

 

First, factorize 117649:

 

117649 = 7 × 7 × 7 × 7 × 7 × 7 = 76

 

Since 7^6 can be written as (73)2, the cube root of 117649 is 72, which equals 49.

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Common Mistakes and How to Avoid Them in the Cube Root of 117649

Finding the perfect cube of a number without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:

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Trying to find cube roots for non-perfect cube numbers.

Children often try to calculate an exact whole number for the cube root of numbers that are not perfect cubes.

For example, they assume that they would get an exact whole number for numbers like 39. To avoid this error, memorize that some numbers don't have a perfect cube root. However, 117649 is a perfect cube, and its cube root is exactly 49.

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Ignoring the exponent form

Most of us might forget the fact that cube root can also be written in exponent form.

For example, forgetting that the cube root of 117649 can be expressed as 117649(1/3). To avoid this error, always learn the forms in which we can express the cube root of a number. plain_heading7 Using incorrect methods for perfect cubes plain_body7 Instead of using prime factorization for perfect cubes, children might end up using approximation methods. For example, they might try to find the cube root of 117649 using iterative methods. Remember that for perfect cubes, prime factorization is the most efficient method.

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Cube Root of 117649 Examples:

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Problem 1

Imagine you have a cube-shaped storage box that has a total volume of 117649 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 company manufactures 117649 cubic meters of material. Calculate the amount of material left after using 50000 cubic meters.

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Explanation

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Problem 3

A container holds 117649 cubic meters of volume. Another container holds a volume of 10000 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 117649 is multiplied by 3, 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 ∛(100000 + 17649).

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Explanation

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FAQs on 117649 Cube Root

1.Can we find the Cube Root of 117649?

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2.Why is Cube Root of 117649 rational?

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3.Is it possible to get the cube root of 117649 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 117649

  • 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: 7 × 7 × 7 = 343, therefore, 343 is a perfect cube.
     
  • Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In a(1/3), ⅓ is the exponent which denotes the cube root of a.
     
  • Radical sign: The symbol that is used to represent a root, which is expressed as (∛).
     
  • Rational number: Numbers that can be expressed as a ratio of two integers. The cube root of 117649 is rational because it is a whole number.
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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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