119 LearnersLast updated on May 26th, 2025
Cube Root of 857375
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 857375 and explain the methods used.
What is the Cube Root of 857375?
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, ∛857375 is written as 857375(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 857375, then y3 can be 857375. Since the cube root of 857375 is an exact value, it is 95.
Finding the Cube Root of 857375
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 857375. 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 857375, which is a perfect cube, we can use the prime factorization method.
Cube Root of 857375 by Prime Factorization Method
Let's find the cube root of 857375 using the prime factorization method.
First, we need to find the prime factors of 857375: 857375 = 5 × 5 × 5 × 7 × 7 × 7 × 11
Grouping the prime factors in triples, we get: (5 × 5 × 5) × (7 × 7 × 7) × 11
Taking one factor from each group, we have: 5 × 7 × 11 = 385
Thus, the cube root of 857375 is 95.
Common Mistakes and How to Avoid Them in the Cube Root of 857375
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 non-perfect cube roots for perfect cube numbers.
Children often overlook that some numbers like 857375 are perfect cubes and try to calculate an approximate value instead of an exact whole number. To avoid this error, recognize that 857375 is a perfect cube, and its cube root is exactly 95.
Mistake 2
Ignoring the exponent form
Most of us might forget the fact that cube root can also be written in exponent form. For example: Forgetting that the cube root of 857375 is 857375^(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 857375 is to divide 857375 by 3. For example: Mistakenly assume 857375 / 3 = cube root of 857375. To avoid this, children should remember that the cube root of 857375 is the number multiplied by itself three times to get 857375.
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 cube root 857375 by estimating. Remember that prime factorization gives the exact cube root for perfect cubes. Since 857375 is a perfect cube, use the prime factorization method.
Mistake 5
Rounding too early
Rounding the cube root too early in the process can lead to errors in the subsequent steps. For example, rounding the cube root of 857375 before finding the exact value. To avoid this, ensure the whole calculation is done, then round the final result if necessary.
Cube Root of 857375 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 857375 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛857375 = 95 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 95 units.
Problem 2
A company manufactures 857375 cubic meters of material. Calculate the amount of material left after using 500000 cubic meters.
The amount of material left is 357375 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount: 857375 - 500000 = 357375 cubic meters.
Problem 3
A bottle holds 857375 cubic meters of volume. Another bottle holds a volume of 20000 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 877375 cubic meters.
Explanation
Explanation: Let’s add the volume of both bottles: 857375 + 20000 = 877375 cubic meters.
Problem 4
When the cube root of 857375 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 95 = 190 The cube of 190 = 6859000
Explanation
When we multiply the cube root of 857375 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(4306875 + 4266875).
∛(4306875 + 4266875) = ∛8573750 ≈ 204.5
Explanation
As shown in the question ∛(4306875 + 4266875), we can simplify that by adding them. So, 4306875 + 4266875 = 8573750. Then we use this step: ∛8573750 ≈ 204.5 to get the answer.
FAQs on 857375 Cube Root
1.Can we find the Cube Root of 857375 exactly?
2.Why is the Cube Root of 857375 rational?
3.Is it possible to get the cube root of 857375 as an approximate 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 857375
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, 95 × 95 × 95 = 857375, therefore, 857375 is a perfect cube. 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 which is expressed as (∛). Rational number: A number that can be expressed as a fraction of two integers. The cube root of 857375 is rational because it is a whole number, 95.
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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.
