Cube Root of 59049
2026-02-21 20:36 Diff
https://brightchamps.com/en-us/math/algebra/cube-root-of-59049

360 Learners

Last updated on August 5, 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 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.

Explore Our Programs

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:

Download Worksheets

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.

Okay, lets begin

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.

Well explained 👍

Problem 2

A company manufactures 59049 cubic meters of material. Calculate the amount of material left after using 27000 cubic meters.

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find ∛(59049 + 59049).

Okay, lets begin

∛(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.

Well explained 👍

FAQs on 59049 Cube Root

1.Can we find the Cube Root of 59049?

Yes, we can find the cube root of 59049 exactly as it is a perfect cube. The cube root of 59049 is 39.

2.Why is the Cube Root of 59049 a rational number?

The cube root of 59049 is rational because it is a whole number, specifically 39.

3.Is it possible to get the cube root of 59049 as an exact number?

Yes, the cube root of 59049 is an exact number, which is 39.

4.Can we find the cube root of any number using prime factorization?

The prime factorization method can be used to calculate the cube root of perfect cube numbers, such as 59049. It helps to break down the number into its prime factors.

5.Is there any formula to find the cube root of a number?

Yes, the formula we use for the cube root of any number ‘a’ is a(1/3).

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.

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.