geometry section 0-9 1112
TRANSCRIPT
Section 0-9Square Roots and Simplifying Radicals
Tuesday, September 20, 2011
Essential Question
How do you evaluate square roots and simplify radical expressions?
Tuesday, September 20, 2011
Vocabulary
1. Product Property:
2. Quotient Property:
Tuesday, September 20, 2011
Vocabulary
1. Product Property: For two numbers a and b ≥ 0,
ab = ai b
2. Quotient Property:
Tuesday, September 20, 2011
Vocabulary
1. Product Property: For two numbers a and b ≥ 0,
ab = ai b
2. Quotient Property: For two numbers a and b ≥ 0,
ab
=a
b
Tuesday, September 20, 2011
Example 1Simplify.
a. 54 b. 126
Tuesday, September 20, 2011
Example 1Simplify.
a. 54 b. 126
9i7
Tuesday, September 20, 2011
Example 1Simplify.
a. 54 b. 126
9i7
9i 7
Tuesday, September 20, 2011
Example 1Simplify.
a. 54 b. 126
9i7
9i 7
3 7
Tuesday, September 20, 2011
Example 1Simplify.
a. 54 b. 126
9i7
9i 7
3 7
9i14
Tuesday, September 20, 2011
Example 1Simplify.
a. 54 b. 126
9i7
9i 7
3 7
9i14
9i 14
Tuesday, September 20, 2011
Example 1Simplify.
a. 54 b. 126
9i7
9i 7
3 7
9i14
9i 14
3 14
Tuesday, September 20, 2011
Example 2Simplify.
a. 80x7y3z4 b. 25a12r8t11
Tuesday, September 20, 2011
Example 2Simplify.
a. 80x7y3z4 b. 25a12r8t11
16i5ix6ixiy2iyiz4
Tuesday, September 20, 2011
Example 2Simplify.
a. 80x7y3z4 b. 25a12r8t11
16i5ix6ixiy2iyiz4
4 x3 yz4 5xy
Tuesday, September 20, 2011
Example 2Simplify.
a. 80x7y3z4 b. 25a12r8t11
16i5ix6ixiy2iyiz4
4 x3 yz4 5xy
25ia12ir8it10it
Tuesday, September 20, 2011
Example 2Simplify.
a. 80x7y3z4 b. 25a12r8t11
16i5ix6ixiy2iyiz4
4 x3 yz4 5xy
25ia12ir8it10it
5a6r4 t 5 14
Tuesday, September 20, 2011
Example 3Simplify.
a. 25
49 b. 81
16
Tuesday, September 20, 2011
Example 3Simplify.
a. 25
49
25
49
b. 81
16
Tuesday, September 20, 2011
Example 3Simplify.
a. 25
49
25
49
57
b. 81
16
Tuesday, September 20, 2011
Example 3Simplify.
a. 25
49
25
49
57
b. 81
16
81
16
Tuesday, September 20, 2011
Example 3Simplify.
a. 25
49
25
49
57
b. 81
16
81
16
94
Tuesday, September 20, 2011
Example 4Simplify.
a. 7
5 b. 9
12
Tuesday, September 20, 2011
Example 4Simplify.
a. 7
5
7
5i
5
5
b. 9
12
Tuesday, September 20, 2011
Example 4Simplify.
a. 7
5
7
5i
5
5
7 55
b. 9
12
Tuesday, September 20, 2011
Example 4Simplify.
a. 7
5
7
5i
5
5
7 55
b. 9
12
9
12i
12
12
Tuesday, September 20, 2011
Example 4Simplify.
a. 7
5
7
5i
5
5
7 55
b. 9
12
9
12i
12
12
9 1212
Tuesday, September 20, 2011
Example 4Simplify.
a. 7
5
7
5i
5
5
7 55
b. 9
12
9
12i
12
12
9 1212
9 4i312
Tuesday, September 20, 2011
Example 4Simplify.
a. 7
5
7
5i
5
5
7 55
b. 9
12
9
12i
12
12
9 1212
9 4i312
18 312
Tuesday, September 20, 2011
Example 4Simplify.
a. 7
5
7
5i
5
5
7 55
b. 9
12
9
12i
12
12
9 1212
9 4i312
18 312
3 32
Tuesday, September 20, 2011
Example 5Simplify.
a. 4
1− 7 i1+ 7
1+ 7
Tuesday, September 20, 2011
Example 5Simplify.
a. 4
1− 7 i1+ 7
1+ 7
4(1+ 7)
(1− 7)(1+ 7)
Tuesday, September 20, 2011
Example 5Simplify.
a. 4
1− 7 i1+ 7
1+ 7
4(1+ 7)
(1− 7)(1+ 7)
4(1+ 7)
(1− 7)(1+ 7)Tuesday, September 20, 2011
Example 5Simplify.
a. 4
1− 7 i1+ 7
1+ 7
4(1+ 7)
(1− 7)(1+ 7)
4(1+ 7)
(1− 7)(1+ 7)
4 + 4 7
1− 7 + 7 − 7
Tuesday, September 20, 2011
Example 5Simplify.
a. 4
1− 7 i1+ 7
1+ 7
4(1+ 7)
(1− 7)(1+ 7)
4(1+ 7)
(1− 7)(1+ 7)
4 + 4 7
1− 7 + 7 − 7
4 + 4 7−6
Tuesday, September 20, 2011
Example 5Simplify.
a. 4
1− 7 i1+ 7
1+ 7
4(1+ 7)
(1− 7)(1+ 7)
4(1+ 7)
(1− 7)(1+ 7)
4 + 4 7
1− 7 + 7 − 7
4 + 4 7−6
2 + 2 7−3
Tuesday, September 20, 2011
Example 5Simplify.
b. 5
6 + 8 i6 − 8
6 − 8
Tuesday, September 20, 2011
Example 5Simplify.
b. 5
6 + 8 i6 − 8
6 − 8
5(6 − 8)
(6 + 8)(6 − 8)
Tuesday, September 20, 2011
Example 5Simplify.
b. 5
6 + 8 i6 − 8
6 − 8
5(6 − 8)
(6 + 8)(6 − 8)
30 − 5 8
6 + 8 − 8 − 8Tuesday, September 20, 2011
Example 5Simplify.
b. 5
6 + 8 i6 − 8
6 − 8
5(6 − 8)
(6 + 8)(6 − 8)
30 − 5 8
6 + 8 − 8 − 8
30 − 5 4i236 − 8
Tuesday, September 20, 2011
Example 5Simplify.
b. 5
6 + 8 i6 − 8
6 − 8
5(6 − 8)
(6 + 8)(6 − 8)
30 − 5 8
6 + 8 − 8 − 8
30 − 5 4i236 − 8
30 −10 228
Tuesday, September 20, 2011
Example 5Simplify.
b. 5
6 + 8 i6 − 8
6 − 8
5(6 − 8)
(6 + 8)(6 − 8)
30 − 5 8
6 + 8 − 8 − 8
30 − 5 4i236 − 8
30 −10 228
15 − 5 214
Tuesday, September 20, 2011
Problem Set
Tuesday, September 20, 2011
Problem Set
p. P20 1-20 all
“Hold yourself responsible for a higher standard than anyone else expects of you. Never excuse yourself.” - Henry Ward Beecher
Tuesday, September 20, 2011