126 LearnersLast updated on May 26th, 2025
Cube Root of 166375
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 166375 and explain the methods used.
What is the Cube Root of 166375?
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, ∛166375 is written as 166375(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 166375, then y³ can be 166375. The cube root of 166375 is an exact value, 55, since 166375 is a perfect cube.
Finding the Cube Root of 166375
Finding the cube root of a number involves 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 166375. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
Since 166375 is a perfect cube, the prime factorization method is suitable for finding its cube root.
Cube Root of 166375 by Prime Factorization
Let's find the cube root of 166375 using the prime factorization method.
First, factorize 166375 into its prime factors:
166375 = 5 × 5 × 5 × 11 × 11 × 11 2.
Group the factors into triples: (5 × 5 × 5) and (11 × 11 × 11) 3.
Take one factor from each group: 5 and 11 4.
Multiply the factors: 5 × 11 = 55
The cube root of 166375 is 55.
Common Mistakes and How to Avoid Them in the Cube Root of 166375
Finding the perfect cube of a number without any errors can be a difficult task for the 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 non-integer cube roots for perfect cube numbers.
Children sometimes assume that numbers like 166375, even if they are perfect cubes, do not result in an integer cube root. To avoid this error, practice recognizing perfect cubes and using prime factorization to confirm the cube root.
Cube Root of 166375 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 166375 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛166375 = 55 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 55 units.
Problem 2
A company manufactures 166375 cubic meters of material. Calculate the amount of material left after using 375 cubic meters.
The amount of material left is 166000 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
166375 - 375 = 166000 cubic meters.
Problem 3
A bottle holds 166375 cubic meters of volume. Another bottle holds a volume of 5000 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 171375 cubic meters.
Explanation
Let’s add the volume of both bottles:
166375 + 5000 = 171375 cubic meters.
Problem 4
When the cube root of 166375 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 55 = 110 The cube of 110 = 1331000
Explanation
When we multiply the cube root of 166375 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(46000 + 12000).
∛(46000 + 12000) = ∛58000 ≈ 38.39
Explanation
As shown in the question ∛(46000 + 12000), we can simplify that by adding them.
So, 46000 + 12000 = 58000.
Then we use this step:
∛58000 ≈ 38.39 to get the answer.
FAQs on 166375 Cube Root
1.Can we find the Cube Root of 166375?
2.Why is Cube Root of 166375 rational?
3.Is it possible to get the cube root of 166375 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 166375?
8.How do technology and digital tools in United States support learning Algebra and Cube Root of 166375?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube Root of 166375
- 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: 5 × 5 × 5 = 125, therefore, 125 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 166375(1/3), ⅓ is the exponent which denotes the cube root of 166375.
- Radical sign: The symbol that is used to represent a root is expressed as (∛).
- Prime factorization: A method of expressing a number as the product of its prime factors. This method is particularly useful for finding cube roots of perfect cubes.
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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.
