1. 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

2. 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

3. 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

4. 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

5. 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

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

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

8. CLASSWORK

9. 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

10. 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

11. 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

12. Classwork