Cube Root of -3
2026-02-28 13:23 Diff
https://brightchamps.com/en-us/math/algebra/cube-root-of-minus-3

194 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 understanding the properties of materials and designing structures. We will now find the cube root of -3 and explain the methods used.

What is the Cube Root of -3?

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, ∛-3 is written as (-3)^(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 -3, then y^3 can be -3. Since the cube root of -3 is not an exact value, we can write it as approximately -1.4422.

Finding the Cube Root of -3

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 -3. The common methods we follow to find the cube root are given below: 

  • Approximation method 
  • Subtraction method
  • Halley’s method

To find the cube root of a non-perfect number, we often follow Halley’s method.

Since -3 is not a perfect cube, we use Halley’s method.

Cube Root of -3 by Halley’s method

Let's find the cube root of -3 using Halley’s method.

The formula is ∛a ≅ x((x^3 + 2a) / (2x^3 + a))

where:

a = the number for which the cube root is being calculated

x = the nearest perfect cube Substituting,

a = -3; x = -1

∛a ≅ -1(((-1)^3 + 2 × (-3)) / (2 × (-1)^3 + (-3)))

∛-3 ≅ -1((-1 - 6) / (-2 - 3)) ∛-3 ≅ -1.442

The cube root of -3 is approximately -1.4422.

Explore Our Programs

Common Mistakes and How to Avoid Them in the Cube Root of -3

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 that students commonly make and the ways to avoid them:

Problem 1

Imagine you have a cube-shaped object that has a total volume of -3 cubic units. Find the length of one side of the object equal to its cube root.

Okay, lets begin

Side of the cube = ∛-3 ≈ -1.44 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 approximately -1.44 units.

Well explained 👍

Problem 2

A company has a material with a volume of -3 cubic meters. If the material is divided equally into 3 parts, what is the volume of each part?

Okay, lets begin

The volume of each part is -1 cubic meters.

Explanation

To find the volume of each part, we need to divide the total volume by 3: -3 / 3 = -1 cubic meters.

Well explained 👍

Problem 3

A container holds -3 cubic liters of liquid. If another container holds 5 cubic liters, what would be the total volume if the containers are combined?

Okay, lets begin

The total volume of the combined containers is 2 cubic liters.

Explanation

Explanation: Let’s add the volume of both containers: -3 + 5 = 2 cubic liters.

Well explained 👍

Problem 4

When the cube root of -3 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?

Okay, lets begin

2 × (-1.44) = -2.88 The cube of -2.88 = -23.87

Explanation

When we multiply the cube root of -3 by 2, it results in a significant change in the volume because the cube increases exponentially.

Well explained 👍

Problem 5

Find ∛(-3 + 5).

Okay, lets begin

∛(-3 + 5) = ∛2 ≈ 1.26

Explanation

As shown in the question ∛(-3 + 5), we can simplify that by adding them. So, -3 + 5 = 2. Then we use this step: ∛2 ≈ 1.26 to get the answer.

Well explained 👍

FAQs on Cube Root of -3

1.Can we find the Cube Root of -3?

No, we cannot find the cube root of -3 exactly as the cube root of -3 is not a whole number. It is approximately -1.4422.

2.Why is the Cube Root of -3 irrational?

The cube root of -3 is irrational because its decimal value goes on without an end and does not repeat.

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

No, the cube root of -3 is not an exact number. It is a decimal that is about -1.4422.

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

Prime factorization method can be used to calculate the cube root of perfect cube numbers, but it is not the right method for non-perfect cube numbers.

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 ≅ x((x^3 + 2a) / (2x^3 + a)).

Important Glossaries for Cube Root of -3

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. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In (-3)^(1/3), ⅓ is the exponent which denotes the cube root of -3. Radical sign: The symbol used to represent a root, expressed as (∛). Irrational number: Numbers that cannot be put in fractional forms are irrational. For example, the cube root of -3 is irrational because its decimal form goes on continuously without repeating the numbers.

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.