Cube Root of -1728
2026-02-21 20:40 Diff
https://brightchamps.com/en-us/math/algebra/cube-root-of-minus-1728

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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 -1728 and explain the methods used.

What is the Cube Root of -1728?

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, ∛-1728 is written as -1728^(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 -1728, then y^3 can be -1728. Since -1728 is a perfect cube, the cube root of -1728 is exactly -12.

Finding the Cube Root of -1728

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 -1728. 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 number, we can use the prime factorization method. Since -1728 is a perfect cube, this method is suitable for finding its cube root.

Cube Root of -1728 by Prime Factorization

Let's find the cube root of -1728 using the prime factorization method. First, we find the prime factors of 1728: 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 Group the factors into triples: (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) Now, take one factor from each group: 2 × 2 × 3 = 12 Since the original number was negative, the cube root is also negative: ∛-1728 = -12 The cube root of -1728 is -12.

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Common Mistakes and How to Avoid Them in the Cube Root of -1728

Finding the cube root 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 the ways to avoid them:

Problem 1

Imagine you have a cube with a total volume of -1728 cubic units. Find the length of one side of the cube equal to its cube root.

Okay, lets begin

Side of the cube = ∛-1728 = -12 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 -12 units.

Well explained 👍

Problem 2

A company processes -1728 cubic units of material. Calculate the amount of material left if 432 cubic units are removed.

Okay, lets begin

The amount of material left is -2160 cubic units.

Explanation

To find the remaining material, we need to subtract the removed material from the total amount: -1728 - 432 = -2160 cubic units.

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Problem 3

A container holds -1728 cubic units of liquid. Another container holds a volume of 256 cubic units. What would be the total volume if the containers are combined?

Okay, lets begin

The total volume of the combined containers is -1472 cubic units.

Explanation

Explanation: Let's add the volume of both containers: -1728 + 256 = -1472 cubic units.

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Problem 4

When the cube root of -1728 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?

Okay, lets begin

2 × (-12) = -24 The cube of -24 = -13824

Explanation

When we multiply the cube root of -1728 by 2, it results in a significant change in volume because the cube increases exponentially.

Well explained 👍

Problem 5

Find ∛(-1296 - 432).

Okay, lets begin

∛(-1296 - 432) = ∛-1728 = -12

Explanation

As shown in the question ∛(-1296 - 432), we simplify by subtracting them: -1296 - 432 = -1728. Then we use this step: ∛-1728 = -12 to get the answer.

Well explained 👍

FAQs on Cube Root of -1728

1.Can we find the Cube Root of -1728?

Yes, we can find the cube root of -1728 exactly because -1728 is a perfect cube. The cube root of -1728 is -12.

2.Why is Cube Root of -1728 rational?

The cube root of -1728 is rational because it is an exact integer: -12.

3.Is it possible to get the cube root of -1728 as an exact number?

Yes, the cube root of -1728 is an exact number: -12.

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

Yes, the prime factorization method can be used to calculate the cube root of negative perfect cube numbers. For example, the cube root of -1728 is -12.

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 -1728

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, -12 × -12 × -12 = -1728, therefore, -1728 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 the quotient or fraction of two integers. The cube root of -1728 is rational because it is -12.

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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.