104 LearnersLast updated on May 26th, 2025
Cube Root of -729
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 -729 and explain the methods used.
What is the Cube Root of -729?
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, ∛(-729) is written as (-729)^(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 -729, then y^3 can be -729. The cube root of -729 is -9 because (-9) × (-9) × (-9) = -729.
Finding the Cube Root of -729
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 -729. 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 like -729, the prime factorization method is very effective.
Cube Root of -729 by Prime Factorization
Let's find the cube root of -729 using the prime factorization method. First, factor -729 into its prime factors: -729 = -1 × 3 × 3 × 3 × 3 × 3 × 3. We group the factors into sets of three: (-1) × (3 × 3 × 3) × (3 × 3 × 3). Each set of three identical factors gives one factor of the cube root. Thus, ∛(-729) = -3. The cube root of -729 is -9.
Common Mistakes and How to Avoid Them in the Cube Root of -729
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 students commonly make and the ways to avoid them:
Mistake 1
Trying to find positive cube roots for negative numbers.
Children often assume that cube roots must be positive even for negative numbers. For example, they might mistakenly think that ∛(-729) should be a positive number. Remember that the cube root of a negative number is negative. For example: ∛(-729) is -9.
Mistake 2
Ignoring the exponent form
Most of us might forget that the cube root can also be written in exponent form. For example, forgetting that the cube root of -729 is written as (-729)^(1/3). To avoid this error, always learn the forms in which we can express the cube root of a number.
Mistake 3
Confusing cube root with division
Some might mistakenly assume the cube root of -729 involves dividing -729 by 3. To avoid this, remember that the cube root of -729 is the number that, when multiplied by itself three times, equals -729.
Mistake 4
Using the wrong method for perfect cubes
Instead of using prime factorization for perfect cubes, children might try more complex methods like Halley’s method. For example, they might overlook the simple factorization of -729. Remember that for perfect cubes, prime factorization is straightforward and effective.
Mistake 5
Rounding too early
Rounding the cube root too early in the process can lead to errors in the subsequent steps. For example, prematurely rounding a calculated cube root of -729 might lead to an incorrect result. To avoid this, ensure the whole calculation is done before rounding.
Cube Root of -729 Examples:
Problem 1
Imagine you have a cube-shaped object with a total volume of -729 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛(-729) = -9 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 -9 units, indicating the direction or nature of the measurement.
Problem 2
A company has a cube of material with a volume of -729 cubic meters. Calculate the amount of material left after using -243 cubic meters.
The amount of material left is -486 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount: -729 - (-243) = -486 cubic meters.
Problem 3
A container has a volume of -729 cubic meters, and another has a volume of -81 cubic meters. What would be the total volume if the containers are combined?
The total volume of the combined containers is -810 cubic meters.
Explanation
Explanation: Add the volume of both containers: -729 + (-81) = -810 cubic meters.
Problem 4
When the cube root of -729 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × (-9) = -18 The cube of -18 = -5832
Explanation
When we multiply the cube root of -729 by 2, it results in a significant increase in magnitude because the cube increases exponentially, resulting in -5832.
Problem 5
Find ∛(-64 - 64).
∛(-64 - 64) = ∛(-128) ≈ -5.04
Explanation
As shown in the question ∛(-64 - 64), we can simplify that by adding them. So, -64 - 64 = -128. Then we use this step: ∛(-128) ≈ -5.04 to get the answer.
FAQs on -729 Cube Root
1.Can we find the Cube Root of -729?
2.Why is Cube Root of -729 a whole number?
3.Is it possible to get the cube root of -729 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 Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Cube Root of -729?
8.How do technology and digital tools in Thailand support learning Algebra and Cube Root of -729?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for Cube Root of -729
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. For example, (-9) × (-9) × (-9) = -729, therefore, -729 is a perfect cube. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In (-729)^(1/3), ⅓ is the exponent which denotes the cube root of -729. Radical sign: The symbol that is used to represent a root which is expressed as (∛). Negative cube root: A negative number that, when multiplied by itself three times, results in a negative perfect cube. For example, ∛(-729) = -9.
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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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