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 592704 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, ∛592704 is written as 592704(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 592704, then y3 can be 592704. Since the cube root of 592704 is an exact value, it can be written as 84.
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 592704. The common methods we follow to find the cube root are given below:
To find the cube root of a perfect number, we often use the prime factorization method. Since 592704 is a perfect cube, we use the prime factorization method.
Let's find the cube root of 592704 using the prime factorization method.
First, we express 592704 as a product of its prime factors: 592704 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 7 × 7 × 7
Now, group the factors in triples: (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) × (7 × 7 × 7)
Each group of three identical numbers represents the cube of a number.
Thus, the cube root of 592704 is: ∛592704 = 2 × 2 × 3 × 7 = 84
The cube root of 592704 is 84.
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 container that has a total volume of 592704 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛592704 = 84 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 84 units.
A company manufactures 592704 cubic meters of material. Calculate the amount of material left after using 123456 cubic meters.
The amount of material left is 469248 cubic meters.
To find the remaining material, we need to subtract the used material from the total amount: 592704 - 123456 = 469248 cubic meters.
A bottle holds 592704 cubic meters of volume. Another bottle holds a volume of 200000 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 792704 cubic meters.
Explanation: Let’s add the volume of both bottles: 592704 + 200000 = 792704 cubic meters.
When the cube root of 592704 is multiplied by 4, calculate the resultant value. How will this affect the cube of the new value?
4 × 84 = 336 The cube of 336 = 3796416
When we multiply the cube root of 592704 by 4, it results in a significant increase in the volume because the cube increases exponentially.
Find ∛(20000+572704).
∛(20000+572704) = ∛592704 ≈ 84
As shown in the question ∛(20000+572704), we can simplify that by adding them.
So, 20000 + 572704 = 592704.
Then, ∛592704 = 84.
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.