Overview
This lecture explains perfect squares, square roots, and methods for finding square roots using geometric, tabular, factorization, and calculator approaches.
Perfect Squares
- A perfect square is the product of a number multiplied by itself (n × n).
- The area of a square with sides of length n is a perfect square (e.g., 4 × 4 = 16).
- Example perfect squares: 1 (1 × 1), 4 (2 × 2), 9 (3 × 3), 16 (4 × 4), 25 (5 × 5), 36 (6 × 6), 49 (7 × 7).
Square Roots
- The square root of a number is the value that, when multiplied by itself, equals that number.
- The symbol √ denotes the square root.
- Example: √16 = 4, since 4 × 4 = 16.
Methods to Find Square Roots
- Geometric Method: Draw a square and count the number of unit squares along one side (e.g., for 144 squares, one side has length 12).
- Table of Perfect Squares: Refer to a list of perfect squares to identify the root (e.g., 12 × 12 = 144, so √144 = 12).
- Prime Factorization: Break down the number into pairs of prime factors (e.g., 144 = 2 × 2 × 2 × 2 × 3 × 3; group pairs, multiply one from each pair: 2 × 2 × 3 = 12).
- Calculator: Use the square root function to find the square root directly.
Key Terms & Definitions
- Perfect Square — A number that is the product of a whole number multiplied by itself.
- Square Root (√) — The value that, when multiplied by itself, gives the original number.
- Prime Factorization — Breaking a number into its smallest prime factors.
Action Items / Next Steps
- Practice finding square roots using all four methods described.
- Review and memorize the first ten perfect squares for quick reference.