160 LearnersLast updated on May 26th, 2025
Cube Root of 729000
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.
What is the Cube Root of 729000?
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 729000
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:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
Since 729000 is a perfect cube, the prime factorization method is the most straightforward way to find its cube root.
Cube Root of 729000 by Prime Factorization Method
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.
Common Mistakes and How to Avoid Them in the Cube Root of 729000
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:
Mistake 1
Trying to find an approximate cube root for a perfect cube number.
Children might try to calculate an approximate value for the cube root of numbers like 729000, which is a perfect cube. To avoid this error, remember that some numbers have an exact cube root, such as 729000, which has a cube root of 90.
Mistake 2
Ignoring the exponent form
Most of us might forget that the cube root can also be written in exponent form.
For example, forgetting that the cube root of 729000 is 729000(1/3). To avoid this error, always learn the forms in which we can express the cube root of a number.
Mistake 3
Confusing cube root with division
To avoid this, students should remember that the cube root of 729000 is the number that, when multiplied by itself three times, gives 729000.
Mistake 4
Using approximation instead of prime factorization for perfect cubes
Instead of using the prime factorization method for perfect cubes, children might use approximation.
For example, they might try to estimate the cube root of 729000. Remember that prime factorization is the best method for perfect cubes. Since 729000 is a perfect cube, use the prime factorization method.
Mistake 5
Rounding too early
Rounding the cube root too early can lead to errors in subsequent steps.
For example, rounding the cube root of 729000 to 89 too early. To avoid this, ensure the whole calculation is done, then round the final result if necessary.
Cube Root of 729000 Examples:
Problem 1
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
Explanation
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.
Problem 2
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.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
729000 - 100000 = 629000 cubic meters.
Problem 3
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.
Explanation
Let’s add the volume of both containers:
729000 + 27000 = 756000 cubic meters.
Problem 4
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
Explanation
When we multiply the cube root of 729000 by 3, the new value's cube significantly increases, resulting in 19683000.
Problem 5
Find ∛(729000 + 27000).
∛(729000 + 27000) = ∛756000 ≈ 91.6
Explanation
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.
FAQs on Cube Root of 729000
1.Can we find the Cube Root of 729000?
2.Why is the Cube Root of 729000 rational?
3.Is it possible to get the cube root of 729000 as an exact number?
4.Can we find the cube root of any number using prime factorization?
5.Is there any formula to find the cube root of a number?
Important Glossaries for Cube Root of 729000
- Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number.
- Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. A perfect cube always results in a whole number. For example, 90 × 90 × 90 = 729000, therefore, 729000 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In 729000(1/3), ⅓ is the exponent which denotes the cube root of 729000.
- Radical sign: The symbol that is used to represent a root is expressed as (∛).
- Rational number: The numbers that can be expressed as a fraction or whole number are rational. For example, the cube root of 729000 is rational because it is a whole number (90).
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Jaskaran Singh Saluja
About the Author
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
