118 LearnersLast updated on May 26th, 2025
Cube Root of 110.592
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 110.592 and explain the methods used.
What is the Cube Root of 110.592?
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, ∛110.592 is written as 110.592^(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 110.592, then y³ can be 110.592. Since the cube root of 110.592 is an exact value, we can write it as 4.8.
Finding the Cube Root of 110.592
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 110.592. 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 110.592 is a perfect cube, we can use this method.
Cube Root of 110.592 by Prime Factorization
Let's find the cube root of 110.592 using the prime factorization method. First, we find the prime factors of 110.592:
110.592 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
Grouping the prime factors in triples:
(2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3)
Taking one factor from each group: 2 × 2 × 3 = 12
Therefore, the cube root of 110.592 is 12.
Common Mistakes and How to Avoid Them in the Cube Root of 110.592
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 students commonly make and the ways to avoid them:
Mistake 1
Trying to find perfect cube roots for non-perfect cube numbers.
Children often try to calculate an exact whole number for the cube root of numbers that are not perfect cubes.
For example, assuming that they would get an exact whole number for numbers like 110.592, if it were not a perfect cube. To avoid this error, remember that some numbers do have a perfect cube root, like 110.592 with a cube root of 4.8.
Mistake 2
Ignoring the exponent form
Most of us might forget the fact that the cube root can also be written in exponent form.
For example, forgetting that the cube root of 110.592 is 110.592^(1/3). To avoid this error, always learn the forms in which we can express the cube root of a number.
Mistake 3
Confusing cube root with division
Assuming the cube root of 110.592 is to divide 110.592 by 3. To avoid this, children should remember that the cube root of 110.592 is the number they multiply by itself three times to get 110.592.
Mistake 4
Using approximation instead of prime factorization for perfect cubes
Instead of using the prime factorization method for perfect cubes, children end up using approximation methods.
For example, they might try to find the cube root of 110.592 by estimation. Remember that prime factorization is ideal for perfect cubes like 110.592.
Mistake 5
Rounding too early
Rounding the cube root too early in the process can lead to errors in subsequent steps.
For example, rounding the cube root of 110.592 to 4.8 too early in the calculation. To avoid this, ensure the whole calculation is done, then round the final result if necessary.
Cube Root of 110.592 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 110.592 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛110.592 = 4.8 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 4.8 units.
Problem 2
A company produces 110.592 cubic meters of material. Calculate the amount of material left after using 40 cubic meters.
The amount of material left is 70.592 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount: 110.592 - 40 = 70.592 cubic meters.
Problem 3
A tank can hold 110.592 cubic meters of water. Another tank can hold 50 cubic meters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 160.592 cubic meters.
Explanation
Explanation: Let’s add the volume of both tanks: 110.592 + 50 = 160.592 cubic meters.
Problem 4
When the cube root of 110.592 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 4.8 = 9.6 The cube of 9.6 = 884.736
Explanation
When we multiply the cube root of 110.592 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(50 + 60.592).
∛(50 + 60.592) = ∛110.592 = 4.8
Explanation
As shown in the question ∛(50 + 60.592), we can simplify that by adding them.
So, 50 + 60.592 = 110.592.
Then we use this step: ∛110.592 = 4.8 to get the answer.
FAQs on 110.592 Cube Root
1.Can we find the Cube Root of 110.592?
2.Why is Cube Root of 110.592 rational?
3.Is it possible to get the cube root of 110.592 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 Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Cube Root of 110.592?
8.How do technology and digital tools in Thailand support learning Algebra and Cube Root of 110.592?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for Cube Root of 110.592
- 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, 3 × 3 × 3 = 27, therefore, 27 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 110.592^(1/3), ⅓ is the exponent which denotes the cube root of 110.592.
- Radical sign: The symbol that is used to represent a root is expressed as (∛).
- Rational number: A number that can be expressed as a fraction or a terminating or repeating decimal. For example, the cube root of 110.592 is rational because it terminates at 4.8.
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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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