118 LearnersLast updated on May 26th, 2025
Cube Root of 250047
A number we multiply by itself three times to obtain the original number is its cube root. It has various applications in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of 250047 and explain the methods used.
What is the Cube Root of 250047?
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, ∛250047 is written as 250047(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 250047, then y3 can be 250047. Since 250047 is a perfect cube, the cube root of 250047 is 63.
Finding the Cube Root of 250047
Finding the cube root of a number is identifying 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 250047. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Estimation method
- Halley's method
Since 250047 is a perfect cube, we can use the prime factorization method to find its exact cube root.
Cube Root of 250047 by Prime Factorization
Let's find the cube root of 250047 using prime factorization.
First, break down 250047 into its prime factors:
250047 = 3 × 3 × 3 × 7 × 7 × 7 × 13 × 13 × 13
Now, group the prime factors in triples to find the cube root: (3 × 7 × 13) × (3 × 7 × 13) × (3 × 7 × 13)
Thus, ∛250047 = 3 × 7 × 13 = 273.
Common Mistakes and How to Avoid Them in the Cube Root of 250047
Finding the cube root of a number without errors can be a challenging task for students. This happens for many reasons. Here are a few mistakes students commonly make and how to avoid them:
Mistake 1
Assuming non-perfect cubes will have whole number roots.
Students often mistakenly seek a whole number cube root for non-perfect cubes like 39. For 250047, ensure to verify if it is a perfect cube before expecting a whole number. Memorize that some numbers, like 250047, do have exact cube roots.
Cube Root of 250047 Examples:
Problem 1
Imagine you have a cube-shaped storage box with a total volume of 250047 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛250047 = 63 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 exactly 63 units.
Problem 2
A company produces 250047 cubic meters of material. How much material would be left after using 50000 cubic meters?
The amount of material left is 200047 cubic meters.
Explanation
To find the remaining material, subtract the used material from the total amount:
250047 - 50000 = 200047 cubic meters.
Problem 3
A container holds 250047 cubic meters of liquid. Another container holds a volume of 50000 cubic meters. What would be the total volume if the containers are combined?
The total volume of the combined containers is 300047 cubic meters.
Explanation
To find the combined volume, add the volume of both containers:
250047 + 50000 = 300047 cubic meters.
Problem 4
When the cube root of 250047 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 63 = 126 The cube of 126 = 2000376
Explanation
Multiplying the cube root of 250047 by 2 results in a higher value, and cubing the new value increases the volume significantly because the cube grows exponentially.
Problem 5
Find ∛(123456 + 250047).
∛(123456 + 250047) = ∛373503 ≈ 72.18
Explanation
As shown in the question ∛(123456 + 250047), we can simplify by adding them.
So, 123456 + 250047 = 373503.
Then use this step: ∛373503 ≈ 72.18 to get the answer.
FAQs on 250047 Cube Root
1.Can we find the Cube Root of 250047?
2.Why is the Cube Root of 250047 rational?
3.Is it possible to get the cube root of 250047 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 States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Cube Root of 250047?
8.How do technology and digital tools in United States support learning Algebra and Cube Root of 250047?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube Root of 250047
- 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, 3 × 3 × 3 = 27.
- 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, expressed as (∛).
- Rational number: Numbers that can be expressed as a fraction of two integers. For example, the cube root of 250047 is rational because it is 63.
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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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