Cube Root of 2744000
2026-02-28 11:55 Diff
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Last updated on August 5, 2025

A number that, when multiplied by itself three times, gives the original number is known as its cube root. This concept has various applications in real life, such as determining the dimensions of cube-shaped objects and in architectural design. We will now find the cube root of 2744000 and explain the methods used.

What is the Cube Root of 2744000?

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, ∛2744000 is written as 2744000(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 2744000, then y³ can be 2744000. Since 2744000 is a perfect cube, we can find its cube root exactly, which is 140.

Finding the Cube Root of 2744000

Finding the cube root of a number involves identifying the number that, when multiplied three times, results in the target number. Now, we will go through the different ways to find the cube root of 2744000. The common methods we follow to find the cube root are given below:

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

To find the cube root of a perfect cube like 2744000, we can use the prime factorization method.

Cube Root of 2744000 by Prime Factorization Method

Let's find the cube root of 2744000 using the prime factorization method.

First, we factor 2744000 into its prime factors: 2744000 = 26 × 53 × 73

Now, for every prime factor, divide the exponent by 3: (26)(1/3) = 22 = 4 (53)(1/3) = 5 (73)(1/3) = 7

Multiply these results together: 4 × 5 × 7 = 140

Therefore, the cube root of 2744000 is 140.

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Common Mistakes and How to Avoid Them in the Cube Root of 2744000

Finding the cube root of a number without any errors can be a challenging task. Here are a few mistakes commonly made and ways to avoid them:

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Problem 1

Imagine you have a cube-shaped toy that has a total volume of 2744000 cubic centimeters. Find the length of one side of the toy which is equal to its cube root.

Okay, lets begin

Side of the cube = ∛2744000 = 140 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 140 units.

Well explained 👍

Problem 2

A company manufactures 2744000 cubic meters of material. Calculate the amount of material left after using 1000000 cubic meters.

Okay, lets begin

The amount of material left is 1744000 cubic meters.

Explanation

To find the remaining material, subtract the used material from the total amount: 2744000 - 1000000 = 1744000 cubic meters.

Well explained 👍

Problem 3

A container holds 2744000 cubic meters of volume. Another container holds a volume of 1000000 cubic meters. What would be the total volume if the containers are combined?

Okay, lets begin

The total volume of the combined containers is 3744000 cubic meters.

Explanation

Explanation: Add the volume of both containers: 2744000 + 1000000 = 3744000 cubic meters.

Well explained 👍

Problem 4

When the cube root of 2744000 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?

Okay, lets begin

2 × 140 = 280 The cube of 280 = 21952000

Explanation

When we multiply the cube root of 2744000 by 2, it results in a significant increase in the volume because the cube of the new value increases exponentially.

Well explained 👍

Problem 5

Find ∛(5000000 + 2744000).

Okay, lets begin

∛(5000000 + 2744000) ≈ ∛7744000 ≈ 198.42

Explanation

As shown in the question ∛(5000000 + 2744000), we can simplify that by adding them. So, 5000000 + 2744000 = 7744000. Then we use this step: ∛7744000 ≈ 198.42 to get the answer.

Well explained 👍

FAQs on 2744000 Cube Root

1.Can we find the Cube Root of 2744000?

Yes, we can find the cube root of 2744000 exactly as it is a perfect cube. The cube root is 140.

2.Why is the Cube Root of 2744000 rational?

The cube root of 2744000 is rational because it results in a whole number, 140, which can be expressed as a ratio of two integers.

3.Is it possible to get the cube root of 2744000 as an exact number?

Yes, the cube root of 2744000 is an exact number, which is 140.

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. For example, 2^3 = 8, which 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’ is a^(1/3).

Important Glossaries for Cube Root of 2744000

  • 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 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 the number of times a number can be multiplied by itself. In a^1/3, ⅓ is the exponent that denotes the cube root of a.
  • Radical sign: The symbol that is used to represent a root is expressed as (∛).
  • Rational number: A rational number is a number that can be expressed as a fraction of two integers, such as the cube root of 2744000, which is 140, a rational 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.

Fun Fact

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