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 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.
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 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: -
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.
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.
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:
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
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.
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.
To find the remaining material, subtract the used material from the total amount:
397 - 100 = 297 cubic meters.
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.
Let’s add the volume of both tanks:
397 + 50 = 447 liters.
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
When we multiply the cube root of 397 by 3, it results in a significant increase in the volume because the cube increases exponentially.
Find ∛(400 + 400).
∛(400 + 400) = ∛800 ≈ 9.28
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.
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.