Simplifying Radicals Product Property 1 Example Simplify FACTOR

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

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

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

radicals Product Property 3. Example: Simplify (FACTOR TREE) x 2 2 2 =4√ 2 √ 32 = ___√___ 8 2 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 √ 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 2 2 n 1. 2 r +6 r + 1 2. a + 10 a 8 -6± √ 28 4 -10± 2 √ 33 2

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

CLASSWORK

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

Simplifying Radical Expressions √x 2 = √x x √y 4 = √y y =x = y 2 √z 10= √z z z z z √a 7 = √a a a a √k 3 = √k k k = k√k = = z 5 3 a √a

Simplifying Radical Expressions √x 2 =x √x 3 = x √x √x 4 = x 2 √x 5 = x 2 √x √x 6 = √x 7 = x 3 √x 8 = √x 9 = x 4 √x 4 y 6 = x 2 y 3 √x 5 y 7 = x 2 y 3√xy √x 5 y 10 = x 2 y 5√x √ 81 x 6 y 3 = 9 x 3 y√y

Classwork