103 LearnersLast updated on May 26th, 2025
Cube Root of -27
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 -27 and explain the methods used.
What is the Cube Root of -27?
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, ∛(-27) is written as (-27)^(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 -27, then y^3 can be -27. Since -27 is a perfect cube, the cube root of -27 is -3.
Finding the Cube Root of -27
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 -27. The common methods we follow to find the cube root are given below: - Prime factorization method - Approximation method - Direct calculation for perfect cubes To find the cube root of a perfect number like -27, we can use direct calculation, recognizing that -27 is a perfect cube.
Cube Root of -27 by Direct Calculation
Let's find the cube root of -27 using direct calculation. Since -27 is a perfect cube, we know that (-3)^3 = -27. Therefore, the cube root of -27 is -3.
Common Mistakes and How to Avoid Them in the Cube Root of -27
Finding the perfect cube of a number without any errors can be a challenging task for students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:
Mistake 1
Trying to find perfect cube roots for non-perfect cube numbers.
Children sometimes mistakenly assume that numbers like -27, which are perfect cubes, do not result in whole numbers. To avoid this error, memorize that some numbers like -27 do indeed have perfect cube roots, which in this case is -3.
Mistake 2
Ignoring the exponent form
Most of us might forget that cube roots can also be written in exponent form. To avoid this error, always learn the forms in which we can express the cube root of a number, such as (-27)^(1/3).
Mistake 3
Confusing cube root with division
To avoid this, children should remember that the cube root of -27 is the number they multiply by itself three times to get -27.
Mistake 4
Using approximation or complex methods instead of direct calculation
Instead of recognizing -27 as a perfect cube, students might try to use methods like approximation, which are unnecessary for perfect cubes. Remember that for perfect cubes like -27, direct calculation is straightforward and accurate.
Mistake 5
Rounding too early
Rounding the cube root too early in the process can lead to errors, but this is less of an issue with perfect cubes like -27. Ensure the whole calculation is done before rounding when necessary.
Cube Root of -27 Examples:
Problem 1
Imagine you have a cube-shaped box that has a total volume of -27 cubic units. Find the length of one side of the box equal to its cube root.
Side of the cube = ∛(-27) = -3 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 -3 units.
Problem 2
A company manufactures -27 cubic meters of material. What would be the volume if they tripled the amount?
The new volume is -81 cubic meters.
Explanation
To find the new volume, we multiply the original amount by 3: -27 * 3 = -81 cubic meters.
Problem 3
If the cube root of -27 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 * (-3) = -6 The cube of -6 = -216
Explanation
When we multiply the cube root of -27 by 2, it results in a new value, -6. The cube of -6 is -216, which shows a significant increase in absolute volume.
FAQs on -27 Cube Root
1.Can we find the Cube Root of -27?
2.Why is Cube Root of -27 not irrational?
3.Is it possible to get the cube root of -27 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 Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Cube Root of -27?
8.How do technology and digital tools in Canada support learning Algebra and Cube Root of -27?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for Cube Root of -27
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 (-27)^(1/3), ⅓ is the exponent which denotes the cube root. Radical sign: The symbol that is used to represent a root is expressed as (∛). Integer: A whole number that can be positive, negative, or zero. The cube root of -27 is an integer (-3).
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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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