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101 LearnersLast updated on December 15, 2025
Cube Root of 370
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 370 and explain the methods used.
What is the Cube Root of 370?
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, ∛370 is written as 370^(1/3).
The cube root is the inverse operation of cubing a number.
For example, if ‘y’ is the cube root of 370, then y³ = 370. Since the cube root of 370 is not an exact integer, we can approximate it as approximately 7.189.
Finding the Cube Root of 370
Finding the cube root of a number involves identifying the number that, when multiplied by itself three times, results in the target number.
We will explore different methods to find the cube root of 370. The common methods include:
- Prime factorization method
- Approximation method
- Subtraction method -
- Halley’s method
Since 370 is not a perfect cube, Halley’s method is often utilized for better approximation.
Cube Root of 370 by Halley’s Method
Let's find the cube root of 370 using Halley’s method.
The formula is: ∛a ≅ x((x³ + 2a) / (2x³ + a)), where: - a = the number for which the cube root is being calculated - x = an initial guess close to the cube root
Substituting,
a = 370;
x = 7 ∛a ≅ 7((7³ + 2 × 370) / (2 × 7³ + 370))
∛370 ≅ 7((343 + 740) / (686 + 370))
∛370 ≅ 7.189
The cube root of 370 is approximately 7.189.
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Common Mistakes and How to Avoid Them in the Cube Root of 370
Finding the cube root of a number without any errors can be challenging for students.
This happens for various reasons.
Here are a few common mistakes and ways to avoid them:
Mistake 1
Trying to find perfect cube roots for non-perfect cube numbers.
Students often try to calculate an exact whole number for the cube root of numbers like 370, which are not perfect cubes.
They may assume that they will get an exact whole number for 370 as they do for 343 (since ∛343 = 7).
To avoid this error, memorize that some numbers don't have a perfect cube root, meaning the cube root of 370 is approximately 7.189.
Mistake 2
Ignoring the exponent form
Many might forget that the cube root can also be written in exponent form.
For example, forgetting that the cube root of 370 is 370^(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
Some assume that finding the cube root of 370 involves dividing 370 by 3.
To avoid this, students should remember that the cube root of 370 is the number you multiply by itself three times to get 370.
Mistake 4
Using prime factorization instead of Halley’s method
Instead of using Halley’s method for non-perfect cubes, students may use prime factorization.
They might attempt to find the cube root of 370 by breaking it down into its prime factors.
Remember, prime factorization can aid in analyzing a number's factors, but it's not the best method for non-perfect cubes.
Since 370 is not a perfect cube, you can 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, we might round the cube root of 370 to 7.2 too early in the calculation.
To avoid this, complete the entire calculation before rounding the final result.
Cube Root of 370 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 370 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛370 = 7.19 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 7.19 units.
Problem 2
A company manufactures 370 cubic meters of material. Calculate the amount of material left after using 120 cubic meters.
The amount of material left is 250 cubic meters.
Explanation
To find the remaining material, subtract the used material from the total amount: 370 - 120 = 250 cubic meters.
Problem 3
A bottle holds 370 cubic meters of volume. Another bottle holds a volume of 80 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 450 cubic meters.
Explanation
Add the volume of both bottles: 370 + 80 = 450 cubic meters.
Problem 4
When the cube root of 370 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 7.19 = 14.38 The cube of 14.38 = 2971.7
Explanation
Multiplying the cube root of 370 by 2 results in a significant increase in volume since the new value is cubed, increasing exponentially.
Problem 5
Find ∛(46 + 324).
∛(46 + 324) = ∛370 ≈ 7.19
Explanation
As shown in the question, ∛(46 + 324), we can simplify this by adding them.
So, 46 + 324 = 370.
Then we use this step: ∛370 ≈ 7.19 to get the answer.
FAQs on Cube Root of 370
1.Can we find the Cube Root of 370?
2.Why is Cube Root of 370 irrational?
3.Is it possible to get the cube root of 370 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 370
- 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 370^(1/3), ⅓ is the exponent which denotes the cube root of 370.
- Radical sign: The symbol that is used to represent a root is expressed as (∛).
- Irrational number: Numbers that cannot be expressed as fractions are irrational. For example, the cube root of 370 is irrational because its decimal form goes on continuously without repeating.
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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.
