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 729000 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, ∛729000 is written as 729000(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 729000, then y3 can be 729000. Since the cube root of 729000 is an exact value, we can write it as 90.
Finding the cube root of a number is to identify 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 729000. The common methods we follow to find the cube root are given below:
Since 729000 is a perfect cube, the prime factorization method is the most straightforward way to find its cube root.
Let's find the cube root of 729000 using the prime factorization method.
First, break down 729000 into its prime factors: 729000 = 23 × 36 × 53 × 73
Since each prime factor has an exponent that is a multiple of 3, we can take the cube root by dividing the exponents by 3:
∛729000 = ∛(23 × 36 × 53 × 73 )
= 2(3/3) × 3(6/3) × 5(3/3) × 7(3/3)
= 2 × 3^2 × 5 × 7
= 2 × 9 × 5 × 7 = 90
Therefore, the cube root of 729000 is 90.
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 ways to avoid them:
Imagine you have a cube-shaped container that has a total volume of 729000 cubic centimeters. Find the length of one side of the cube.
Side of the cube = ∛729000 = 90 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 90 units.
A company manufactures 729000 cubic meters of material. Calculate the amount of material left after using 100000 cubic meters.
The amount of material left is 629000 cubic meters.
To find the remaining material, we need to subtract the used material from the total amount:
729000 - 100000 = 629000 cubic meters.
Two containers hold 729000 and 27000 cubic meters of volume, respectively. What would be the total volume if the containers are combined?
The total volume of the combined containers is 756000 cubic meters.
Let’s add the volume of both containers:
729000 + 27000 = 756000 cubic meters.
When the cube root of 729000 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?
3 × 90 = 270 The cube of 270 = 19683000
When we multiply the cube root of 729000 by 3, the new value's cube significantly increases, resulting in 19683000.
Find ∛(729000 + 27000).
∛(729000 + 27000) = ∛756000 ≈ 91.6
As shown in the question ∛(729000 + 27000), we can simplify that by adding them.
So, 729000 + 27000 = 756000.
Then we use this step: ∛756000 ≈ 91.6 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.