BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon104 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

Cube Root of -8

Professor Greenline Explaining Math Concepts

A number that, when multiplied by itself three times, results in the original number is its cube root. Cube roots have various applications in real life, such as calculating dimensions in construction and designing objects. We will now find the cube root of -8 and explain the methods used.

Cube Root of -8 for Singaporean Students
Professor Greenline from BrightChamps

What is the Cube Root of -8?

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, ∛-8 is written as (-8)^(1/3). The cube root is the opposite operation of finding the cube of a number. For example, assume ‘y’ as the cube root of -8, then y^3 = -8. The cube root of -8 is -2, because (-2) × (-2) × (-2) = -8.

Professor Greenline from BrightChamps

Finding the Cube Root of -8

Finding the cube root of a number involves identifying the number that must be multiplied three times to result in the target number. Now, we will explore the different ways to find the cube root of -8. The common methods include: - Prime factorization method - Direct calculation for perfect cubes Since -8 is a perfect cube, we can easily find its cube root using the direct calculation method.

Professor Greenline from BrightChamps

Cube Root of -8 by Direct Calculation

Let's find the cube root of -8 using direct calculation. Since -8 is a perfect cube, we know: - The cube root of -8 is -2 because (-2) × (-2) × (-2) = -8. The cube root of -8 is -2.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in Finding the Cube Root of -8

Finding the cube root of a number can sometimes be challenging. Here are common mistakes students make and ways to avoid them:

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Confusing negative cube roots with positive values

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Sometimes, students assume that the cube root of a negative number will also be negative or positive without understanding the operation. For example, the cube root of -8 is -2, not -4 or 2. To avoid this, remember the properties of cube roots: the root of a negative perfect cube is negative.

Mistake 2

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Ignoring the exponent form

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Many people forget that the cube root can also be represented in exponential form. For example, the cube root of -8 is (-8)^(1/3). To avoid this mistake, always learn the different forms in which we can express the cube root of a number.

Mistake 3

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Confusing cube root with division

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Some students mistakenly think finding the cube root of -8 involves dividing -8 by 3. To avoid this, remember that the cube root of -8 is the number that, when cubed, equals -8.

Mistake 4

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Rounding answers inappropriately for perfect cubes

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Rounding is not necessary when dealing with perfect cubes like -8. The cube root of -8 is exactly -2. To prevent errors, recognize when a number is a perfect cube and use direct calculations for exact results.

Mistake 5

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Applying prime factorization unnecessarily

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

For perfect cubes like -8, students may try to use prime factorization unnecessarily. Remember, prime factorization is more useful for non-perfect cubes. For perfect cubes, direct calculation is more efficient.

arrow-right
Max from BrightChamps Saying "Hey"

Cube Root of -8 Examples:

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Imagine you have a cube-shaped toy with a total volume of -8 cubic units. Find the length of one side of the cube.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Side of the cube = ∛-8 = -2 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 -2 units.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

If a company manufactures -8 cubic meters of a substance, what is the side length of the cube if the material is shaped into a cube?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The side length of the cube is -2 meters.

Explanation

To find the side length of the cube, calculate the cube root of the volume: ∛-8 = -2 meters.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

A storage unit has a volume of -8 cubic meters. What is the length of one side of the unit?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The length of one side of the storage unit is -2 meters.

Explanation

The side length is found by calculating the cube root of the volume: ∛-8 = -2 meters.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

What is the result when the cube root of -8 is multiplied by 3?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

3 × (-2) = -6

Explanation

Multiplying the cube root of -8 by 3 gives -6. This operation scales the side length by a factor of three.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find ∛(-16 - 8).

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

∛(-16 - 8) = ∛-24 ≈ -2.884

Explanation

First, add the numbers inside the cube root: -16 - 8 = -24. Then calculate the cube root: ∛-24 ≈ -2.884.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQs on Cube Root of -8

1.Can we find the Cube Root of -8 exactly?

Math FAQ Answers Dropdown Arrow

2.Why is Cube Root of -8 considered a real number?

Math FAQ Answers Dropdown Arrow

3.Is the cube root of -8 rational?

Math FAQ Answers Dropdown Arrow

4.Can we find the cube root of any number by direct calculation?

Math FAQ Answers Dropdown Arrow

5.What is the significance of the negative cube root?

Math FAQ Answers Dropdown Arrow

6.How does learning Algebra help students in Singapore make better decisions in daily life?

Math FAQ Answers Dropdown Arrow

7.How can cultural or local activities in Singapore support learning Algebra topics such as Cube Root of -8?

Math FAQ Answers Dropdown Arrow

8.How do technology and digital tools in Singapore support learning Algebra and Cube Root of -8?

Math FAQ Answers Dropdown Arrow

9.Does learning Algebra support future career opportunities for students in Singapore?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for Cube Root of -8

Cube root: The number that, when multiplied three times by itself, results in the given number. Perfect cube: A number that is the product of multiplying a number three times by itself. For example, (-2) × (-2) × (-2) = -8, so -8 is a perfect cube. Exponent: An exponent indicates how many times a number is multiplied by itself. In cube roots, the exponent is ⅓. Radical sign: The symbol (∛) used to represent the root of a number. Rational number: A number that can be expressed as a fraction of two integers, like -2/1 for the cube root of -8.

Professor Greenline from BrightChamps

About BrightChamps in Singapore

At BrightChamps, we understand algebra is far more than symbols—it’s a gateway to countless possibilities! We aim to help kids across Singapore master vital math skills, focusing today on the Cube Root of -8 with a special focus on cube roots—in an engaging, easy-to-follow, and enjoyable way. Whether your child is figuring out the speed of a roller coaster at Universal Studios Singapore, keeping track of scores at a local football match, or managing their allowance for the latest gadgets, mastering algebra builds confidence for everyday life. Our interactive lessons keep learning simple and fun. Since kids in Singapore learn in different ways, we customize our teaching to fit each learner’s needs. From the vibrant city streets to scenic gardens, BrightChamps brings math alive, making it relevant and exciting throughout Singapore. Let’s make cube roots a fun part of every child’s math journey!
Math Teacher Background Image
Math Teacher Image

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.

Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom