Cube Root of 1331000
2026-02-28 18:03 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. 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 1331000 and explain the methods used.

What is the Cube Root of 1331000?

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, ∛1331000 is written as 1331000(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 1331000, then y³ can be 1331000. The cube root of 1331000 is an exact value, which is 110.

Finding the Cube Root of 1331000

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 1331000. The common methods we follow to find the cube root are given below:

- Prime factorization method

- Estimation method

- Halley’s method

To find the cube root of a perfect cube number, we can follow the prime factorization method. Since 1331000 is a perfect cube, prime factorization is an efficient method here.

Cube Root of 1331000 by Prime Factorization

Let's find the cube root of 1331000 using the prime factorization method.

First, we perform prime factorization of 1331000: 1331000 = 2 × 2 × 2 × 5 × 5 × 5 × 11 × 11 × 11

Grouping the prime factors in triples: (2 × 2 × 2) × (5 × 5 × 5) × (11 × 11 × 11)

Taking the cube root of each group gives us: ∛1331000 = 2 × 5 × 11 = 110

Therefore, the cube root of 1331000 is 110.

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Common Mistakes and How to Avoid Them in Finding the Cube Root of 1331000

Finding the perfect cube of a number without any errors can be a challenging 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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Problem 1

Imagine you have a cube-shaped container that has a total volume of 1331000 cubic centimeters. Find the length of one side of the cube.

Okay, lets begin

Side of the cube = ∛1331000 = 110 cm

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 exactly 110 cm.

Well explained 👍

Problem 2

A company manufactures 1331000 cubic meters of material. Calculate the amount of material left after using 100000 cubic meters.

Okay, lets begin

The amount of material left is 1231000 cubic meters.

Explanation

To find the remaining material, we need to subtract the used material from the total amount: 1331000 - 100000 = 1231000 cubic meters.

Well explained 👍

Problem 3

A container holds 1331000 cubic meters of volume. Another container holds a volume of 1000 cubic meters. What would be the total volume if the containers are combined?

Okay, lets begin

The total volume of the combined containers is 1332000 cubic meters.

Explanation

Explanation: Let’s add the volume of both containers: 1331000 + 1000 = 1332000 cubic meters.

Well explained 👍

Problem 4

When the cube root of 1331000 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?

Okay, lets begin

2 × 110 = 220 The cube of 220 = 10648000

Explanation

When we multiply the cube root of 1331000 by 2, it results in a significant increase in the volume because the cube increases exponentially.

Well explained 👍

Problem 5

Find ∛(1000000+331000).

Okay, lets begin

∛(1000000+331000) = ∛1331000 = 110

Explanation

As shown in the question ∛(1000000+331000), we can simplify that by adding them. So, 1000000 + 331000 = 1331000. Then we take the cube root to get the answer, which is 110.

Well explained 👍

FAQs on Cube Root of 1331000

1.Can we find the Cube Root of 1331000?

Yes, we can find the cube root of 1331000 exactly as it is a perfect cube. The cube root of 1331000 is 110.

2.Why is the Cube Root of 1331000 a rational number?

The cube root of 1331000 is rational because it can be expressed as an exact whole number, which is 110.

3.Is it possible to get the cube root of 1331000 as an exact number?

Yes, the cube root of 1331000 is an exact number, which is 110.

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 effectively. For example, 1331000 is a perfect cube, so prime factorization works well.

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

Yes, the cube root of any number ‘a’ can be expressed as a^(1/3), which is the exponential form of expressing a cube root.

Important Glossaries for Cube Root of 1331000

  • 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, 110 × 110 × 110 = 1331000, therefore, 1331000 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: A number that can be expressed as a fraction or an exact value. For example, the cube root of 1331000 is rational because it is exactly 110.

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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.

Fun Fact

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