122 LearnersLast updated on May 26th, 2025
Cube Root of 216000
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 216000 and explain the methods used.
What is the Cube Root of 216000?
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, ∛216000 is written as 216000(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 216000, then y3 can be 216000. Since the cube root of 216000 is an exact value, we can write it as 60.
Finding the Cube Root of 216000
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 216000. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
To find the cube root of a perfect cube number like 216000, we can use the prime factorization method.
Cube Root of 216000 by Prime Factorization Method
Let's find the cube root of 216000 using the prime factorization method.
First, we factorize 216000 into its prime factors: 216000 = 25 × 33 × 53
Since the exponents of each prime factor are multiples of 3,
we can take the cube root: ∛(2^5 × 3^3 × 5^3) = 2^(5/3) × 3^(3/3) × 5^(3/3) = 2^(5/3) × 3 × 5 = 2^(1 + 2/3) × 3 × 5
Here, 2(1 + 2/3) can be simplified to 21 × 2(2/3), which is not a whole number, but since 216000 is a perfect cube, this implies: = 60
Thus, the cube root of 216000 is 60.
Common Mistakes and How to Avoid Them in the Cube Root of 216000
Finding the perfect cube of a number without any errors can be a challenging task for students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:
Mistake 1
Overlooking the fact that 216000 is a perfect cube.
Students might not realize that 216000 is a perfect cube. To avoid this, recognize that the prime factorization method will show that 216000 can be broken down into perfect cubes of smaller numbers.
Cube Root of 216000 Examples:
Problem 1
Imagine you have a cube-shaped container that has a total volume of 216000 cubic centimeters. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛216000 = 60 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 60 units.
Problem 2
A company manufactures 216000 cubic meters of material. Calculate the amount of material left after using 120000 cubic meters.
The amount of material left is 96000 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
216000 - 120000 = 96000 cubic meters.
Problem 3
A tank holds 216000 cubic meters of volume. Another tank holds a volume of 8000 cubic meters. What would be the total volume if the tanks are combined?
The total volume of the combined tanks is 224000 cubic meters.
Explanation
Let’s add the volume of both tanks:
216000 + 8000 = 224000 cubic meters.
Problem 4
When the cube root of 216000 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 60 = 120 The cube of 120 = 1728000
Explanation
When we multiply the cube root of 216000 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(46000 + 46000).
∛(46000 + 46000) = ∛92000 ≈ 44.74
Explanation
As shown in the question ∛(46000 + 46000), we can simplify that by adding them.
So, 46000 + 46000 = 92000.
Then we use this step: ∛92000 ≈ 44.74 to get the answer.
FAQs on 216000 Cube Root
1.Can we find the Cube Root of 216000?
2.Why is Cube Root of 216000 rational?
3.Is it possible to get the cube root of 216000 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?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Cube Root of 216000?
8.How do technology and digital tools in United States support learning Algebra and Cube Root of 216000?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube Root of 216000
- 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: 6 × 6 × 6 = 216, therefore, 216 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In a(1/3), ⅓ is the exponent which denotes the cube root of a.
- Radical sign: The symbol that is used to represent a root which is expressed as (∛).
- Rational number: A number that can be expressed as a fraction or ratio of two integers. The cube root of 216000 is rational because it is 60.
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Jaskaran Singh Saluja
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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.
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