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 262144 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, ∛262144 is written as 262144(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 262144, then y3 can be 262144. Since 262144 is a perfect cube, its cube root is exactly 64.
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 262144. The common methods we follow to find the cube root are given below:
To find the cube root of a perfect cube number like 262144, we often use the prime factorization method or direct calculation. Since 262144 is a perfect cube, we can easily find its cube root using straightforward calculations.
Let's find the cube root of 262144 using the prime factorization method.
The prime factorization of 262144 is 2^18.
We can group the factors in triples of three identical numbers: (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2)
This gives us (23)6 = 643.
Thus, the cube root of 262144 is 64.
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 the students commonly make and the ways to avoid them:
Imagine you have a cube-shaped storage container that has a total volume of 262144 cubic centimeters. Find the length of one side of the cube.
Side of the cube = ∛262144 = 64 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 exactly 64 units.
A storage facility has a cubic volume of 262144 cubic meters. Calculate how many smaller cubes with a side length of 32 meters can fit inside.
The number of smaller cubes that can fit inside is 8.
The volume of one smaller cube is 32^3 = 32768 cubic meters.
The number of such smaller cubes that can fit inside is 262144 / 32768 = 8.
A company produces 262144 cubic meters of material. Calculate the amount of material left after using 100000 cubic meters.
The amount of material left is 162144 cubic meters.
To find the remaining material, we need to subtract the used material from the total amount: 262144 - 100000 = 162144 cubic meters.
A storage box holds a volume of 262144 cubic meters. Another storage box holds a volume of 32768 cubic meters. What would be the total volume if the boxes are combined?
The total volume of the combined boxes is 294912 cubic meters.
Let’s add the volume of both boxes: 262144 + 32768 = 294912 cubic meters.
Find ∛(100000 + 162144).
∛(100000 + 162144) = ∛262144 = 64
As shown in the question ∛(100000 + 162144), we can simplify that by adding them.
So, 100000 + 162144 = 262144.
Then we use this step: ∛262144 = 64 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.