Cubes and Cube Roots – 8th Grade Mathematics
Cubes and Cube Roots
1. Introduction to Cubes
Definition: The cube of a number n is defined as n3 = n × n × n.
Examples
13 = 1
23 = 2 × 2 × 2 = 8
33 = 3 × 3 × 3 = 27
43 = 4 × 4 × 4 = 64
2. Properties of Cubes
- The cube of a positive number is positive.
- The cube of zero is zero: 03 = 0.
- The cube of a negative number is negative: (-n)3 = -n3.
3. Introduction to Cube Roots
Definition: The cube root of a number x is a number y such that y3 = x. It is denoted as √[3]{x} or x1/3.
4. Finding Cube Roots
Cube roots can be found through:
- Prime factorization method
- Estimation
- Using calculators
5. Examples of Finding Cube Roots
Find the cube root of 64:
64 = 4 × 4 × 4, so √[3]{64} = 4.
Find the cube root of 27:
27 = 3 × 3 × 3, so √[3]{27} = 3.
Conclusion
Understanding cubes and cube roots is essential for solving problems in mathematics. Practice these concepts with various numbers to strengthen your skills!