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Cyberpunk Math Lab: The Non-Linear World FREE
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Perfect Squares & Square Roots
Learning Objectives
- Simplify square roots
- Solve equations with squares
- Rationalize denominators
Key Concepts
Square Root
√a is the non-negative number whose square is a
Perfect Square
A number whose square root is an integer
Theory
**Perfect squares:** 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144…
**Simplifying:** √(ab) = √a × √b
- √72 = √(36 × 2) = 6√2
**Solving x² = k:**
- x = ±√k (two solutions!)
**Rationalizing:** 1/√a = √a/a
Examples
Simplify √50
Solution: √(25×2) = 5√2