105 LearnersLast updated on May 26th, 2025
Cube Root of 17576
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 17576 and explain the methods used.
What is the Cube Root of 17576?
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, ∛17576 is written as 17576(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 17576, then y3 can be 17576. Since the cube root of 17576 is an exact value, we can write it as 26.
Finding the Cube Root of 17576
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 17576. 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 number, we often use the prime factorization method. Since 17576 is a perfect cube, we can use this method.
Cube Root of 17576 by Prime Factorization Method
Let's find the cube root of 17576 using the prime factorization method.
The prime factorization of 17576 is:
17576 = 2 × 2 × 2 × 13 × 13 × 13
Grouping the prime factors in triples: (2 × 2 × 2) × (13 × 13 × 13)
Taking one factor from each group gives us: 2 × 13 = 26
Therefore, the cube root of 17576 is 26.
Common Mistakes and How to Avoid Them in the Cube Root of 17576
Finding the perfect cube of a number without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:
Mistake 1
Trying to find cube roots for non-perfect cube numbers using the wrong method.
Children sometimes try to calculate an exact whole number for the cube root of numbers like 17576, which is a perfect cube, but they might use inappropriate methods.
For example: They might assume that 17576 is not a perfect cube and try to use approximation methods. To avoid this error, recognize when a number is a perfect cube and apply the prime factorization method.
Cube Root of 17576 Examples:
Problem 1
Imagine you have a cube-shaped box that has a total volume of 17576 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛17576 = 26 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 26 units.
Problem 2
A company manufactures 17576 cubic meters of material. Calculate the amount of material left after using 12345 cubic meters.
The amount of material left is 5231 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
17576 - 12345 = 5231 cubic meters.
Problem 3
A storage unit holds 17576 cubic meters of volume. Another storage unit holds a volume of 8000 cubic meters. What would be the total volume if the units are combined?
The total volume of the combined storage units is 25576 cubic meters.
Explanation
Let’s add the volume of both storage units:
17576 + 8000 = 25576 cubic meters.
Problem 4
When the cube root of 17576 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 26 = 52
The cube of 52 = 140608
Explanation
When we multiply the cube root of 17576 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(23000 + 3200).
∛(23000 + 3200) = ∛26200 ≈ 29.66
Explanation
As shown in the question ∛(23000 + 3200), we can simplify that by adding them.
So, 23000 + 3200 = 26200.
Then we use this step: ∛26200 ≈ 29.66 to get the answer.
FAQs on 17576 Cube Root
1.Can we find the Cube Root of 17576?
2.Why is Cube Root of 17576 rational?
3.Is it possible to get the cube root of 17576 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?
Important Glossaries for Cube Root of 17576
- 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: 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 17576(1/3), ⅓ is the exponent which denotes the cube root of 17576.
- 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 ratio of two integers. The cube root of 17576 is rational because it is a whole number: 26.
Explore More algebra
Previous to Cube Root of 17576
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.
