Cubes and Cube Roots 8 Mathematics — Revision Notes
Cubes are numbers raised to the third power, while cube roots are the inverse operation. Unlike square roots, cube roots of negative numbers are negative,
TL;DR: Cubes are numbers raised to the third power, while cube roots are the inverse operation. Unlike square roots, cube roots of negative numbers are negat…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Cubes are numbers raised to the third power, while cube roots are the inverse operation. Unlike square roots, cube roots of negative numbers are negative,
Key Points to Remember
- A perfect cube is a number obtained by multiplying an integer by itself three times
- Examples of perfect cubes: 1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125
- Perfect cubes can be positive or negative, unlike perfect squares
- The cube root of a number is the value that when multiplied by itself three times gives the original number
- The cube root of positive numbers is positive, and of negative numbers is negative
- Every real number has exactly one cube root
- Prime factorization method helps find cube roots by grouping factors in threes
- Cube roots of negative numbers follow the rule: ∛(-n) = -∛n
- The digits 0 through 9 cubed end in 0, 1, 8, 7, 4, 5, 6, 3, 2, 9 respectively
- Pattern exists in last digits of cubes, useful for identifying cubes
- Cube root of decimal numbers can be found using prime factorization
- Cube roots are used in volume calculations and solving cubic equations
Important Formulas
- Perfect Cube: n³ = n × n × n
- Cube Root: ∛n³ = n
- Property: ∛(abc) = ∛a × ∛b × ∛c
- Negative Cube Root: ∛(-n³) = -n
Key Terms
- Perfect Cube: Integer that is the cube of another integer
- Cube Root: Value that when multiplied by itself three times equals the original number
- Prime Factorization: Expression of a number as a product of prime numbers
- Radical: Expression containing a root symbol, like ∛n
- Digit Root: The last digit of a number, used to identify perfect cubes
- Real Number: Any number on the number line, including integers, fractions, and irrational numbers
Frequently Asked Questions
What is the difference between cubes and cube roots?
Cubes are numbers raised to the third power, like 2³ = 8. Cube roots are the inverse operation finding the number that was cubed, like ∛8 = 2
Can cube roots be negative?
Yes, cube roots can be negative. The cube root of a negative number is negative, following the rule ∛(-n) = -∛n. For example, ∛(-8) = -2
How do you find cube roots of large numbers using prime factorization?
Find the prime factorization of the number, then group the prime factors into groups of three. Multiply one factor from each group to get the cube root
More 8 Mathematics Revision Notes
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →