Product Property (FACTOR TREE) Simplifying Radicals Product Property (FACTOR TREE) 1. Example: Simplify √12 = ___√___ 2 3 √12 4 3 Single stays inside 2 Pair goes outside

Product Property (FACTOR TREE) YOUR TURN! Product Property (FACTOR TREE) 2. Example: Simplify √8 = ___√___ 2 2 √8 4 2 Single stays inside 2 Pair goes outside

Product Property (FACTOR TREE) radicals Product Property (FACTOR TREE) 3. Example: Simplify √24 = ___√___ 2 6 √24 6 4 2 3 2 x Pair goes outside 6 stays inside

radicals Product Property (FACTOR TREE) 2 2 x 3. Example: Simplify √32 = ___√___ 2 =4√2 8 4 4 2 2 2 single stays inside Pairs multiplied outside

Practice √12 √20 √28 2√8 3√12 -4√18 √432 √242 √150 √12 = 2√3 √20 = 2√5 √12 = 2√3 √20 = 2√5 √28 = 2√7 2√8 = 4√2 3√12 = 6√3 -4√18 = -12√2 √432 = 12√3 √242 = 11√2 √150 = 5√6

WARM-UP -50√3 3√2 5√2 1. 2r2 +6r + 1 2. a2 + 10a - 8 -6± √28 4 -10±2 √33 2

Multiplication Property Example 1: √2 X √7 = √14 Example 2: √7 X √7 = √49 = 7 Example 3: √2 X √4 = √8 = 2√2

CLASSWORK

Practice -2 -4 1. x2 +6x+8=0, x=___ x=___ 1. √45 2. √48 3. √108 4. √98 Simplify the following radicals: Multiply the following radicals, then simplify: Solve for x by completing the square: 1. x2 +6x+8=0, x=___ x=___ 1. √45 2. √48 3. √108 4. √98 1. (√4) (√3) 2. (-√5) (√9) 3√5 4√3 6√3 7√2 -3√5 2√3 -4 -2

Simplifying Radical Expressions = √x x = y2 √y4 = √y y y y √z10 = √z z z z z z z z z z = z5 √a7 = √a a a a a a a = a3√a √k3 = √k k k = k√k

Simplifying Radical Expressions √x4y6 = x2 y3 √x3 = x √x √x4 = x2 √x5y7 = x2y3√xy √x5 = x2 √x √x6 √x5y10 = x3 = x2y5√x = x3 √x √x7 √x8 √81x6y3 = 9x3y√y = x4 = x4 √x √x9

Classwork