113 LearnersLast updated on May 26th, 2025
Cube Root of 59049
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 59049 and explain the methods used.
What is the Cube Root of 59049?
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, ∛59049 is written as 59049(1/3). The cube root is just the opposite operation of finding the cube of a number. For example, assume ‘y’ is the cube root of 59049, then y3 can be 59049. Since the cube root of 59049 is an exact value, it is 39.
Finding the Cube Root of 59049
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 59049. 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 non-perfect cube number, we often follow Halley’s method. However, since 59049 is a perfect cube, we can use the prime factorization method.
Cube Root of 59049 by Prime Factorization
Let's find the cube root of 59049 using the prime factorization method.
First, express 59049 as a product of its prime factors:
59049 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3
Group the factors into triples: (3 × 3 × 3) × (3 × 3 × 3) × (3 × 3 × 3)
Take one factor from each group: 3 × 3 × 3 = 27
Thus, the cube root of 59049 is 27.
Common Mistakes and How to Avoid Them in the Cube Root of 59049
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 students commonly make and the ways to avoid them:
Mistake 1
Trying to find perfect cube roots for non-perfect cube numbers.
Students sometimes try to calculate an exact whole number for the cube root of numbers that are not perfect cubes.
For example, they assume they would get an exact whole number for non-perfect cubes. To avoid this error, understand that not all numbers have a perfect cube root, but 59049 does, which is 39.
Cube Root of 59049 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 59049 cubic centimeters. Find the length of one side of the cube.
Side of the cube = ∛59049 = 39 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 39 units.
Problem 2
A company manufactures 59049 cubic meters of material. Calculate the amount of material left after using 27000 cubic meters.
The amount of material left is 32049 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount: 59049 - 27000 = 32049 cubic meters.
Problem 3
A bottle holds 59049 cubic centimeters of volume. Another bottle holds a volume of 8000 cubic centimeters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 67049 cubic centimeters.
Explanation
Let’s add the volume of both bottles: 59049 + 8000 = 67049 cubic centimeters.
Problem 4
When the cube root of 59049 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 39 = 78 The cube of 78 = 474552
Explanation
When we multiply the cube root of 59049 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(59049 + 59049).
∛(59049 + 59049) = ∛118098 ≈ 48.96
Explanation
As shown in the question ∛(59049 + 59049), we can simplify that by adding them.
So, 59049 + 59049 = 118098.
Then we use this step: ∛118098 ≈ 48.96 to get the answer.
FAQs on 59049 Cube Root
1.Can we find the Cube Root of 59049?
2.Why is the Cube Root of 59049 a rational number?
3.Is it possible to get the cube root of 59049 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 Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Cube Root of 59049?
8.How do technology and digital tools in Australia support learning Algebra and Cube Root of 59049?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for Cube Root of 59049
- 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, 3 × 3 × 3 = 27, therefore, 27 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 number.
- 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 a whole number. The cube root of 59049 is rational because it equals 39.
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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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