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 778 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, ∛778 is written as (778{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 778, then (y3) can be 778. Since the cube root of 778 is not an exact value, we can write it as approximately 9.218.
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 778. 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 778 is not a perfect cube, we use Halley’s method.
Let's find the cube root of 778 using Halley’s method.
The formula is [sqrt[3]{a} approx xleft(frac{x3+2a}{2x3+a}right)]
where: a = the number for which the cube root is being calculated
x = the nearest perfect cube
Substituting, a = 778;
x = 9
[sqrt[3]{778} approx 9 left(frac{93 + 2 × 778}{2 × 93 + 778}right)]
[sqrt[3]{778} approx 9.218]
The cube root of 778 is approximately 9.218.
Finding the perfect cube of a number without any errors can be a difficult task for students. This happens for many 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 778 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛778 = 9.218 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 9.218 units.
A factory produces 778 cubic meters of a chemical solution. If 200 cubic meters are used, calculate the remaining solution.
The amount of remaining solution is 578 cubic meters.
To find the remaining solution, we need to subtract the used volume from the total amount:
778 - 200 = 578 cubic meters.
A tank holds 778 cubic meters of water. Another tank holds a volume of 150 cubic meters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 928 cubic meters.
Let’s add the volume of both tanks:
778 + 150 = 928 cubic meters.
When the cube root of 778 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 9.218 = 27.654 The cube of 27.654 = 21,133.8
When we multiply the cube root of 778 by 3, it results in a significant increase in the volume because the cube increases exponentially.
Find ∛(100 + 678).
∛(100 + 678) = ∛778 ≈ 9.218
As shown in the question ∛(100 + 678), we can simplify that by adding them.
So, 100 + 678 = 778.
Then we use this step: ∛778 ≈ 9.218 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.