126 LearnersLast updated on May 26th, 2025
Cube Root of 397
A number we multiply by itself three times to get the original number is its cube root. It has various applications in real life, such as determining the dimensions of cube-shaped objects and designing structures. We will now find the cube root of 397 and explain the methods used.
What is the Cube Root of 397?
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, ∛397 is written as 397(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 397, then y³ can be 397. Since the cube root of 397 is not an exact value, we can write it as approximately 7.368.
Finding the Cube Root of 397
Finding the cube root of a number involves identifying 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 397. The common methods we use to find the cube root are given below: -
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
To find the cube root of a non-perfect cube number, we often use Halley’s method. Since 397 is not a perfect cube, we use Halley’s method.
Cube Root of 397 by Halley’s Method
Let's find the cube root of 397 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 = the nearest perfect cube
Substituting, a = 397; x = 7
∛a ≅ 7((7³ + 2 × 397) / (2 × 7³ + 397))
∛397 ≅ 7((343 + 794) / (686 + 397))
∛397 ≅ 7.368
The cube root of 397 is approximately 7.368.
Common Mistakes and How to Avoid Them in the Cube Root of 397
Finding the perfect cube of a number without any errors can be a challenging task for students. This happens for many reasons. Here are a few mistakes commonly made 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 397, which are not perfect cubes. For example, they assume that they would get an exact whole number for 397 like they do for 343 (since ∛343 = 7). To avoid this error, remember that some numbers don't have a perfect cube root, meaning the cube root of 397 is approximately 7.37.
Mistake 2
Ignoring the exponent form
Many people might forget that the cube root can also be written in exponent form. For example, forgetting that the cube root of 397 is 397(1/3). To avoid this error, always learn the forms in which we can express the cube root of a number.
Mistake 3
Confusing the cube root with division
Assuming the cube root of 397 is to divide 397 by 3 is incorrect. For example, mistakenly assume ∛397 = 397/3. To avoid this, students should remember that the cube root of 397 is the number that, when multiplied by itself three times, gives 397.
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. For example, they might try to find the cube root of 397 by breaking it down into its prime factors. Remember, prime factorization can help analyze a number's factors, but it's not the best method for non-perfect cubes. Since 397 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 the subsequent steps. For example, one might round the cube root of 397 to 7.4 too early in the calculation. To avoid this, complete the entire calculation, then round the final result.
Cube Root of 397 Examples:
Problem 1
Imagine you have a cube-shaped box that has a total volume of 397 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛397 = 7.37 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 7.37 units.
Problem 2
A company manufactures 397 cubic meters of material. Calculate the amount of material left after using 100 cubic meters.
The amount of material left is 297 cubic meters.
Explanation
To find the remaining material, subtract the used material from the total amount:
397 - 100 = 297 cubic meters.
Problem 3
A tank holds 397 liters of water. Another tank holds a volume of 50 liters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 447 liters.
Explanation
Let’s add the volume of both tanks:
397 + 50 = 447 liters.
Problem 4
When the cube root of 397 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 7.37 = 22.11
The cube of 22.11 = 10795.4
Explanation
When we multiply the cube root of 397 by 3, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(400 + 400).
∛(400 + 400) = ∛800 ≈ 9.28
Explanation
As shown in the question ∛(400 + 400),
we can simplify that by adding them.
So, 400 + 400 = 800.
Then we use this step: ∛800 ≈ 9.28 to get the answer.
FAQs on 397 Cube Root
1.Can we find the Cube Root of 397?
2.Why is the Cube Root of 397 irrational?
3.Is it possible to get the cube root of 397 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 Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Cube Root of 397?
8.How do technology and digital tools in Philippines support learning Algebra and Cube Root of 397?
9.Does learning Algebra support future career opportunities for students in Philippines?
Important Glossaries for Cube Root of 397
- 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 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 is expressed as (∛).
- Irrational number: Numbers that cannot be expressed as a simple fraction are irrational. For example, the cube root of 397 is irrational because its decimal form goes on continuously without repeating.
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Jaskaran Singh Saluja
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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.
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