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100 LearnersLast updated on April 28th, 2025
Cube Root of 185193
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 185193 and explain the methods used.
What is the Cube Root of 185193?
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, ∛185193 is written as 185193(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 185193, then y³ can be 185193. Since 185193 is a perfect cube, its cube root is an exact value, 57.
Finding the Cube Root of 185193
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 185193. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Estimation method
- Subtraction method
- Halley’s method
Since 185193 is a perfect cube, we can use the prime factorization or estimation method to find its cube root efficiently.
Cube Root of 185193 by Prime Factorization
Let's find the cube root of 185193 using the prime factorization method.
The prime factors of 185193 are:
185193 = 3 × 3 × 3 × 19 × 19 × 19
Grouping the factors in triples, we get (3 × 3 × 3) and (19 × 19 × 19).
Hence, ∛185193 = 3 × 19 = 57.
The cube root of 185193 is 57.
Common Mistakes and How to Avoid Them in the Cube Root of 185193
Cube Root of 185193 Examples:
Problem 1
Imagine you have a cube-shaped box that has a total volume of 185193 cubic centimeters. Find the length of one side of the box equal to its cube root.
Explanation
Problem 2
A company manufactures 185193 cubic meters of material. Calculate the remaining amount after using 57193 cubic meters.
Explanation
Problem 3
A tank holds 185193 cubic meters of water. Another tank holds a volume of 40000 cubic meters. What would be the total volume if the tanks are combined?
Explanation
Problem 4
When the cube root of 185193 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
Explanation
Problem 5
Find ∛(47025 + 138168).
Explanation
FAQs on 185193 Cube Root
1.Can we find the Cube Root of 185193?
2.Why is Cube Root of 185193 not irrational?
3.Is it possible to get the cube root of 185193 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 185193
- 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, 57 × 57 × 57 = 185193, therefore, 185193 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 185193(1/3), ⅓ is the exponent which denotes the cube root of 185193.
- Radical sign: The symbol that is used to represent a root is expressed as (∛).
- Exact number: A number that is precise and not estimated or rounded. For example, the cube root of 185193 is exactly 57.
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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.
