Last updated on May 26th, 2025
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.
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 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.
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.
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:
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
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.
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.
To find the remaining material, we need to subtract the used material from the total amount: 797 - 300 = 497 cubic meters.
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: Let’s add the volume of both tanks: 797 + 150 = 947 cubic meters.
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
When we multiply the cube root of 797 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Find ∛(400+397).
∛(400+397) = ∛797 ≈ 9.28
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.
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.
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.
: He loves to play the quiz with kids through algebra to make kids love it.