1. Radical Expressions Simplification, Rationalization and Operations

2. What are radicals? A radical is an expression that expresses the square roots, cube roots etc. The following are examples of radicals: 2, 5,12 36, −27, 410 257, 184, 3325 36, 510, 438

3. Simplifying Radicals We say that a square root radical is simplified, or in its simplest form, when the radicand (the number inside) has no square factors. The following are examples of radicals in simplest form: 3, 25, 26 The following are examples of radicals in simplest form: 16, 312, 28

4. How do we simplify radicals? STEP 1: Find the prime factors of the radicand. Try these: 18 20 24 27 30 40 72 120

5. How do we simplify radicals? STEP 1: Find the prime factors of the radicand. Try these: 18 = 2·3·3 20 =2·2·5 24 = 2·2·3·2 27 = 3·3·3 30 = 5·2·3 40 = 2·2·2·5 72 = 2·2·2·3·3 120 = 2·2·3·2·5

6. How do we simplify radicals? STEP 2: For each pair of same prime factor, send it outside the radical. Try these: 2·3·3 2·2·5 2·2·3·2 3·3·3 5·2·3 2·2·2·5 2·2·2·3·3 2·2·3·2·5

7. How do we simplify radicals? STEP 2: For each pair of same prime factor, send it outside the radical. Try these: 2·3·3=32 2·2·5 = 25 2·2·3·2 = 26 3·3·3 = 33 5·2·3 = 30 2·2·2·5 = 210 2·2·2·3·3 = 62 2·2·3·2·5 = 230