117 LearnersLast updated on May 26th, 2025
Cube Root of 797
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 determining the volume of cube-shaped objects and in architectural design. We will now find the cube root of 797 and explain the methods used.
What is the Cube Root of 797?
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, ∛797 is written as 797^(1/3). The cube root is the inverse operation of cubing a number. For example, assume ‘y’ as the cube root of 797, then y^3 can be 797. Since the cube root of 797 is not an exact value, we can write it as approximately 9.2835.
Finding the Cube Root of 797
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 797. 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 number, we often use Halley’s method. Since 797 is not a perfect cube, we use Halley’s method.
Cube Root of 797 by Halley’s Method
Let's find the cube root of 797 using Halley’s method. The formula is: ∛a ≅ x((x^3 + 2a) / (2x^3 + a)) where: a = the number for which the cube root is being calculated x = the nearest perfect cube Substituting, a = 797; x = 9 ∛a ≅ 9((9^3 + 2 × 797) / (2 × 9^3 + 797)) ∛797 ≅ 9((729 + 2 × 797) / (2 × 729 + 797)) ∛797 ≅ 9.283 The cube root of 797 is approximately 9.2835.
Common Mistakes and How to Avoid Them in the Cube Root of 797
Finding the perfect cube of a number without any errors can be a challenging task for students. This happens for various reasons. Here are a few mistakes students commonly make and the 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 797, which are not perfect cubes. For example, they assume they would get an exact whole number for 797 like they get for 729 (since ∛729 = 9). To avoid this error, memorize that some numbers don't have a perfect cube root, and the cube root of 797 is approximately 9.2835.
Mistake 2
Ignoring the exponent form
Many might forget that the cube root can also be written in exponent form. For example, they might forget that the cube root of 797 is 797^(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 797 is to divide 797 by 3 is a common error. For example, mistakenly assuming 797/3 = 265.6667 as the cube root. To avoid this, students should remember that the cube root of 797 is the number they multiply by itself three times to get 797.
Mistake 4
Using prime factorization instead of Halley’s method
Instead of using Halley’s method for non-perfect cubes, students may attempt to use prime factorization. For example, they might try to find the cube root of 797 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 797 is a non-perfect cube, it's better to use 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 797 to 9.3 too early in the calculation. To avoid this, ensure the whole calculation is completed before rounding the final result.
Cube Root of 797 Examples:
Problem 1
Imagine you have a cube-shaped container that has a total volume of 797 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛797 ≈ 9.28 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 9.28 units.
Problem 2
A company manufactures 797 cubic meters of material. Calculate the amount of material left after using 300 cubic meters.
The amount of material left is 497 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount: 797 - 300 = 497 cubic meters.
Problem 3
A tank holds 797 cubic meters of water. Another tank holds a volume of 150 cubic meters of water. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 947 cubic meters.
Explanation
Explanation: Let’s add the volume of both tanks: 797 + 150 = 947 cubic meters.
Problem 4
When the cube root of 797 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 9.28 ≈ 18.56 The cube of 18.56 ≈ 6398.5
Explanation
When we multiply the cube root of 797 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(400+397).
∛(400+397) = ∛797 ≈ 9.28
Explanation
As shown in the question ∛(400+397), we can simplify that by adding them. So, 400 + 397 = 797. Then we use this step: ∛797 ≈ 9.28 to get the answer.
FAQs on 797 Cube Root
1.Can we find the Cube Root of 797?
2.Why is Cube Root of 797 irrational?
3.Is it possible to get the cube root of 797 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 Indonesia make better decisions in daily life?
7.How can cultural or local activities in Indonesia support learning Algebra topics such as Cube Root of 797?
8.How do technology and digital tools in Indonesia support learning Algebra and Cube Root of 797?
9.Does learning Algebra support future career opportunities for students in Indonesia?
Important Glossaries for Cube Root of 797
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 797^(1/3), ⅓ is the exponent which denotes the cube root of 797. Radical sign: The symbol that is used to represent a root is expressed as (∛). Irrational number: Numbers that cannot be put in fractional forms are irrational. For example, the cube root of 797 is irrational because its decimal form goes on continuously without repeating.
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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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