Chapter 9 section 2 operations on radical expressions

1
Chapter 9section 2operations on radical
expressions
2
Objective 1

• To simplify radical expressions

3
Review 1st 15 Perfect squares
4
Review
Simplify the Square Root
5
Review
Simplify the Square Root
6
Review
Simplify the Square Root
7
Simplifying Square Roots
Perfect Squares
Not Perfect Squares
8
Example 1
Simplify the Square Root
Whats the biggest number here that will go into
54 evenly?
9 x 6
9
Example 1
Simplify the Square Root
10
Example 2
Simplify the Square Root
Whats the biggest number here that will go into
72 evenly?
36 x 2
11
Example 2
Simplify the Square Root
12
Example 3
Simplify the Square Root
Whats the biggest number here that will go into
80 evenly?
16 x 5
13
Example 3
Simplify the Square Root
14
Remember
Always choose the biggest number from this list.

Always put the number from this list (the perfect
square) first.
15

• Now, lets simplify square roots with variables
  only

16
review
To take square root of variable expressions,
divide the exponents by 2.
17

• What if the exponents cant be divided by 2?
• (They are not even)

18

• What if the exponents cant be divided by 2?
• (They are not even)

1. Rewrite all variables with odd exponents. (Take
   it down)
2. Circle the perfect squares. (even exponents)
3. Take square root of perfect squares. They go
   outside the radical.
4. Leave everything else inside the radical.

19

• What if the exponents cant be divided by 2?
• (They are not even)

1. Rewrite all variables with odd exponents. (Take
   it down)
2. Circle the perfect squares. (even exponents)
3. Take square root of perfect squares. They go
   outside the radical.
4. Leave everything else inside the radical.

20
Example 4
Simplify the Square Root
Rewrite the variables with odd exponents.
21
Example 4
Simplify the Square Root
Circle the perfect squares (even exponents)
22
Example 4
Simplify the Square Root
23
Example 5
Simplify the Square Root
Rewrite the variables with odd exponents.
24
Example 5
Simplify the Square Root
Circle the perfect squares (even exponents)
25
Example 5
Simplify the Square Root
26

• Now, lets simplify square roots with
  coefficients and variables.

27
Example 6
Simplify the Square Root
Rewrite 18 with largest perfect square factor. 9
x 2
28
Example 6
Simplify the Square Root
Rewrite the variables with odd exponents.
29
Example 6
Simplify the Square Root
Circle the perfect squares
30
Example 7
Simplify the Square Root
Rewrite 20 with largest perfect square factor. 4
x 5
31
Example 7
Simplify the Square Root
Rewrite the variables with odd exponents.
32
Example 7
Simplify the Square Root
Circle the perfect squares
33
Objective 2

• To add or subtract radical expressions

34
Review
To add or subtract expressions with the same
variable, just add or subtract the coefficients.
35
Square roots
To add or subtract expressions with the same
root, just add or subtract the number in front of
the root.
36
Example 8
To add or subtract expressions with the same
root, just add or subtract the number in front of
the root.
37
Example 9
Add the Square Roots
38
Example 10
Subtract the Square Roots
39
Example 11
Add Square Roots
40
Example 12
Add and Subtract the Square Roots
41
Example 12
Add and Subtract the Square Roots
42
Example 13
Subtract the Square Roots
43
Example 14
Add and Subtract the Square Roots
44
Example 15
Add the Cube Roots
45

• Click on the link for 9.2 Part 2
• to view the rest of the Powerpoint.