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 finding the volume of cube-shaped objects and designing structures. We will now find the cube root of 278 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, ∛278 is written as 278^(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 278, then y^3 can be 278. Since the cube root of 278 is not an exact value, we can write it as approximately 6.482.
Finding the cube root of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of 278. The common methods we follow to find the cube root are given below:
To find the cube root of a non-perfect number, we often follow Halley’s method. Since 278 is not a perfect cube, we use Halley’s method.
Let's find the cube root of 278 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 = 278;
x = 6
∛a ≅ 6((6^3 + 2 × 278) / (2 × 6^3 + 278))
∛278 ≅ 6((216 + 556) / (432 + 278))
∛278 ≅ 6.481
The cube root of 278 is approximately 6.482.
Finding the perfect cube of a number without any errors can be a difficult task for the students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:
Imagine you have a cube-shaped toy that has a total volume of 278 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛278 = 6.48 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 6.48 units.
A company manufactures 278 cubic meters of material. Calculate the amount of material left after using 78 cubic meters.
The amount of material left is 200 cubic meters.
To find the remaining material, we need to subtract the used material from the total amount:
278 - 78 = 200 cubic meters.
A bottle holds 278 cubic meters of volume. Another bottle holds a volume of 50 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 328 cubic meters.
Let’s add the volume of both bottles:
278 + 50 = 328 cubic meters.
When the cube root of 278 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 6.48 = 12.96 The cube of 12.96 = 2175.93
When we multiply the cube root of 278 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Find ∛(100+178).
∛(100+178) = ∛278 ≈ 6.48
As shown in the question ∛(100+178), we can simplify that by adding them.
So, 100 + 178 = 278.
Then we use this step:
∛278 ≈ 6.48 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.