113 LearnersLast updated on May 26th, 2025
Cube Root of 2744000
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.
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:
Mistake 1
Trying to find cube roots without recognizing perfect cubes.
People often try to calculate a cube root without realizing whether the number is a perfect cube.
For example, they might not recognize that 2744000 is a perfect cube. To avoid this error, check if the number can be expressed as a product of primes with exponents divisible by 3.
Cube Root of 2744000 Examples:
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.
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.
Problem 2
A company manufactures 2744000 cubic meters of material. Calculate the amount of material left after using 1000000 cubic meters.
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.
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?
The total volume of the combined containers is 3744000 cubic meters.
Explanation
Explanation: Add the volume of both containers: 2744000 + 1000000 = 3744000 cubic meters.
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?
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.
Problem 5
Find ∛(5000000 + 2744000).
∛(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.
FAQs on 2744000 Cube Root
1.Can we find the Cube Root of 2744000?
2.Why is the Cube Root of 2744000 rational?
3.Is it possible to get the cube root of 2744000 as an exact number?
4.Can we find the cube root of any number using prime factorization?
5.Is there any formula to find the cube root of a number?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Cube Root of 2744000?
8.How do technology and digital tools in United Kingdom support learning Algebra and Cube Root of 2744000?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
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.
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