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141 LearnersLast updated on December 15, 2025
Cube Root of 42.875
A number that, when multiplied by itself three times, results in the original number is known as its cube root. It has various applications in real life, such as determining the dimensions of cube-shaped objects and engineering designs. We will now find the cube root of 42.875 and explain the methods used.
What is the Cube Root of 42.875?
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 (โ), and the exponent we use is โ .
In exponential form, โ42.875 is written as 42.875^(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 42.875, then y³ can be 42.875. Since the cube root of 42.875 is not an exact value, we can write it as approximately 3.488.
Finding the Cube Root of 42.875
Finding the cube root of a number is to identify the number that must be multiplied three times to result in the target number.
Now, we will go through the different ways to find the cube root of 42.875.
The common methods we follow to find the cube root are given below:
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Prime factorization method
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Approximation method
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Subtraction method
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Halley’s method
To find the cube root of a non-perfect number, we often follow Halley’s method.
Since 42.875 is not a perfect cube, we use Halley’s method.
Cube Root of 42.875 by Halleyโs Method
Let's find the cube root of 42.875 using Halley’s method.
The formula is โa ≅ x((x³ + 2a) / (2x³ + a))
where: a = the number for which the cube root is being calculated
x = the nearest perfect cube Substituting,
a = 42.875;
x = 3
โa ≅ 3((3³ + 2 × 42.875) / (2 × 3³ + 42.875))
โ42.875 ≅ 3((27 + 2 × 42.875) / (2 × 27 + 42.875))
โ42.875 ≅ 3.488
The cube root of 42.875 is approximately 3.488.
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Common Mistakes and How to Avoid Them in the Cube Root of 42.875
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 that 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 like 42.875, which are not perfect cubes.
They might assume they would get an exact whole number for 42.875 like they get for 27 (since 27 is a perfect cube).
To avoid this error, remember that some numbers don't have a perfect cube root, and the cube root of 42.875 is approximately 3.488.
Mistake 2
Ignoring the exponent form
Most of us might forget that the cube root can also be written in exponent form.
For example, forgetting that the cube root of 42.875 can be written as 42.875^(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 42.875 is to divide 42.875 by 3.
For example, mistakenly assuming that 42.875 / 3 is the cube root. To avoid this, remember that the cube root of 42.875 is the number that, when multiplied by itself three times, equals 42.875.
Mistake 4
Using prime factorization instead of Halley’s method
Instead of using Halley’s method for non-perfect cubes, students might use prime factorization.
For example, they might try to find the cube root of 42.875 by breaking it down into its prime factors. Remember that prime factorization can help analyze a number's factors, but it's not the best method for non-perfect cubes. Since 42.875 is a non-perfect cube, use either the approximation method or Halley’s method.
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 42.875 to 3.5 too early in the calculation. To avoid this, ensure the whole calculation is done, then round the final result.
Cube Root of 42.875 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 42.875 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = โ42.875 = 3.49 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 approximately 3.49 units.
Problem 2
A company manufactures 42.875 cubic meters of material. Calculate the amount of material left after using 15 cubic meters.
The amount of material left is 27.875 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
42.875 - 15 = 27.875 cubic meters.
Problem 3
A bottle holds 42.875 cubic meters of volume. Another bottle holds a volume of 7 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 49.875 cubic meters.
Explanation
Let’s add the volume of both bottles:
42.875 + 7 = 49.875 cubic meters.
Problem 4
When the cube root of 42.875 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 3.49 = 10.47 The cube of 10.47 = 1147.56
Explanation
When we multiply the cube root of 42.875 by 3, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find โ(50 + 50).
โ(50 + 50) = โ100 ≈ 4.64
Explanation
As shown in the question โ(50 + 50), we can simplify that by adding them.
So, 50 + 50 = 100.
Then we use this step:
โ100 ≈ 4.64 to get the answer.
FAQs on 42.875 Cube Root
1.Can we find the Cube Root of 42.875?
2.Why is Cube Root of 42.875 irrational?
3.Is it possible to get the cube root of 42.875 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 42.875
- 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 42.875^(1/3), โ
is the exponent which denotes the cube root of 42.875.
- Radical sign: The symbol that is used to represent a root is expressed as (โ).
- Irrational number: Numbers that cannot be put in fractional forms are irrational. For example, the cube root of 42.875 is irrational because its decimal form goes on continuously without repeating the numbers.
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.
