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Last updated on April 30th, 2025

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Cube Root of 1000000

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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 1000000 and explain the methods used.

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What is the Cube Root of 1000000?

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, ∛1000000 is written as 1000000(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 1000000, then y3 can be 1000000. Since 1000000 is a perfect cube, the cube root of 1000000 is exactly 100.cube root of 1000000

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Finding the Cube Root of 1000000

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 1000000. The common methods we follow to find the cube root are given below:

 

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

 

Since 1000000 is a perfect cube, the prime factorization method can be effectively used.

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Cube Root of 1000000 by Prime Factorization Method

Let's find the cube root of 1000000 using the prime factorization method. First, express 1000000 as a product of its prime factors: 1000000 = 106 = (2 × 5)6 = 26 × 5^6

 

To find the cube root, we take one-third of the powers of each prime factor: ∛1000000 = 2^(6/3) × 5^(6/3) = 2^2 × 5^2 = 4 × 25 = 100 Therefore, the cube root of 1000000 is 100.

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Common Mistakes and How to Avoid Them in the Cube Root of 1000000

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Cube Root of 1000000 Examples:

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Problem 1

Imagine you have a cube-shaped toy that has a total volume of 1000000 cubic centimeters. Find the length of one side of the cube.

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Explanation

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Problem 2

A company manufactures 1000000 cubic meters of material. Calculate the amount of material left after using 500000 cubic meters.

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Explanation

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Problem 3

A bottle holds 1000000 cubic centimeters of volume. Another bottle holds a volume of 200000 cubic centimeters. What would be the total volume if the bottles are combined?

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Explanation

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Problem 4

When the cube root of 1000000 is multiplied by 2, 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 ∛(500000+500000).

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Explanation

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FAQs on 1000000 Cube Root

1.Can we find the Cube Root of 1000000?

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2.Why is Cube Root of 1000000 rational?

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3.Is it possible to get the cube root of 1000000 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 1000000

  • 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. For example: 10 × 10 × 10 = 1000, therefore, 1000 is a perfect cube.

 

  • Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 1000000(1/3), ⅓ is the exponent which denotes the cube root.

 

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

 

  • Rational number: The numbers that can be expressed as a fraction or whole numbers are rational. For example, the cube root of 1000000 is rational because it is a whole number, 100.
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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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