Chapter 7
“Roots and Radicals”
Date
Section
Topic
11/11
7.4
nth Roots (Perfect)
11/12
7.4
nth Roots ( Not Perfect)
11/13
7.5
11/16
7.5
11/17
7.5
11/18
11/19
7.6
11/20
7.7
11/23
7.7
Operations with Radical Expressions
(Adding and Subtracting)
Operations with Radical Expressions
(Multiplying and Dividing)
Operations with Radical Expressions
(Conjugates)
Assignment
Pg. 434 (13-23o, 27-35o, 47-53o, 70)
Worksheet #2
p. 443 (9,10, 30-33)
p. 443 (5-8, 18, 21, 26-29, 37-40, 69)
Pg. 443 (3, 4, 13-16, 22-25)
QUIZ (7.4-7.5)
Worksheet #6
Rational Exponents
Worksheet #7
Solving Radical Equations and
Inequalties
Solving Radical Equations and
Inequalties
Pg. 456 (1-12, 76-79)
Pg. 457 (23-33o)
11/24
REVIEW
Review Packet
11/30
REVIEW
TBD
12/01
CHAPTER 7 TEST
Advanced Algebra
Section 7.4 Notes Day 1 Notes
nth Roots
Goal – Students will be able to simplify radical expressions.
You should know:
The REAL nth roots of b are:
32  9
so 3 is the square root of 9
(3)2  9
so -3 is the square root of 9
33  27
so 3 is the cube root of 27
If given
n
n
b and  n b then:
b then:
n is even and b>0
 n is even and b<0


 n is odd and b>0

 n is odd and b<0
 one positive and one negative root
 empty set, no solution, 
 one positive root
 one negative root
Etc...
Therefore, if a n  b then a is the nth root of b
What is the square root of 64? x 2  64 so x  8
If you are asked for 64 , the symbol
wants only the positive answer (because the writer of the problem knows
what answer he/she wants for a solution).
IF the
is in the problem when you begin, we take the positive answer.
IF the IF the
is in the problem when you begin, we take the negative answer.
is added to the problem by you or me, then we need to add in the  sign.
So
64  8 (the
is in it from the beginning).
Find the value of following. Watch where the + or – signs are.
1. a.
49 
b.  49 
c.
49 
d.  49 
2. a.
3
64 
b.
3
64 
c.  3 64 
Now we are going to add in variables. How do you simplify the variables when they are under the root symbol?
3.  81n 
2
4.  121a b 
5.  169x 
2
8.  (8 x  3) 
6 2
4
6.
81b2 
4
7.  ( x  1) 
9.
x2  8x  16 
10.
3
8n9 
11.
3
125x6 
12.
3
m3n3 
13.
5
32x 5 y10 
14.
4
m4 
15.
4
(an) 4 
16.
6
( xy 2 )6 
17.
6
(3  y 2 )18 
Advanced Algebra
Section 7.4 Notes Day 2 Notes
nth Roots
Do you know your
PERFECT SQUARES?
12=
Goal – Students will be able to simplify radical expressions.
22=
32=
Simplify.
24a3b2
1.
64a 2b3c4
2.
54x 4 y 5 z 7
3.
42=
52=
62=
72=
82=
4.
3
3
40x y
5
5.
3
3 7
54a b
6.
4
8
32x y
6
92=
102=
112=
122=
7.
3
54x 2 y 9
8.
4
462m12 n
9.
216x12 y 3 z 5
132=
Do you know your
CUBE VALUES?
13=
23=
10.
3
128x9 y12
11.
5
243w15 z10
12.
4
1875x8 y 4
33=
43=
53=
63=
73=
Advanced Algebra
Section 7.5 Day 1 Notes
Adding Radical Expresssions
Goal – Students will be able to add and subtract radical expressions.
Rules for Adding/Subtracting radical expressions.
Simplify.
1. 4  3 5  7  2 5
2. 2 3  5  7 3  2
3. 4 27  3 3  48
4. 5 6  3 24  150
5. 2 180  2 72  200  3 45
6.
48  10  100  98
8.
128  3 80  2 450
7.
108  2 147  5 27
Advanced Algebra
Section 7.5 Day 2 Notes
Multiplying Radical Expresssions
Goal – Students will be able to multiple radical expressions.
Rules for Mulitplying radical expressions.
Simplify.
1.
10

2 6

3. 2 15 3  5
5.

7 2x 4 y 3



2. 5 2 3 3  4 5


4. 2 10 5  4 2

2
6. 3x 2 8 xy 2



2
What process do you need to use when multiplying binomials?
7.
3  2  4 
10

8.
5  3 5  3 
9.


5 2 7 4 2 5

10.


5 3 2 2 5 4 2

Advanced Algebra
Section 7.5 Day 3 Notes
Dividing with Radical Expresssions
Goal – Students will be able to rationalize radical expressions.
Steps to Rationalize
Can a radical be left in the demonimator? Why/why not?
What is RATIONALIZATION?
1.
3.
3
y8
x7
2.
2
9x
4.
x6
y7
4
6
5x
What happens when there are 2 terms in the denominator and at least one of them contains a
What is the CONJUGATE?
Simplify
5.
7.
2
5 1
1 5
3 3
6.
8.
3
5 2
3 22 5
5 3
?
Advanced Algebra
Section 7.6 Notes
Rational Exponents
Goal – Students will be write expressions in both radical and rational exponent forms.
Look at the following statements. What can you conclude?
xx
1
2
3
xx
1
3
n
xx
1
n
Evaluate.
1
1. a.
64 3 
b.
36 2 
1
n
 1
b  b  bn 
 
m
n
m

1
4

1
2
2. a. 625
b.
49


m
What can you conclude about this statement?
Simplify the expression.
2
3. a. 8 3 
5
6
b. 64 
1
2
4. a. 7 3 7 3
2
3
b. 64 64
1
6
Write each expression in radical form.
2
1
3
5. 7
3
6. 4
7.
1
3 7
x 
8.
2
3 7
y 
Write each radical in exponential form.
9.
11.
13.
4
64
3
10.
3x 9 y
12.
7  4 75
14.
5
27
4
3
36x 2 y 3
62  4 63
Advanced Algebra
Section 7.7 Day 1 Notes
Solving Radical Equations
Steps for Solving
Radical Equations
Goal – Students will be able to solve different types of radical equations.
1. Get one
alone
2. Square both sides of the equation
Solving radical equations. MUST check answers!
1.
2 y 1  3  0
3. 12  3m  7  5
3. If
2. 9  x  1  1
4.
3
4x 1  3  0
still in problem:
A. Get
alone
B. Square each side again
4. Solve and check
Solving radical equations. MUST check answers!
5. 3 4 2 x  6  6  0
1
6. 4  3x  6  4  12  0
Steps for Solving
Radical Equations
1. Get one
alone
2. Square both sides of the equation
3. If
still in problem:
A. Get
alone
B. Square each side again
4. Solve and check
1
7.
 9 x 11 2  x  1
1
8.
 6 x  53  2  3
Advanced Algebra
Section 7.7 Day 2 Notes
Solving Radical Equations
Steps for Solving
Radical Equations
Goal – Students will be able to solve different types of radical equations.
1. Get one
alone
2. Square both sides of the equation
Solving radical equations. MUST check answers!
3. If
1.
3.
x  8  x  35  3
x  15  5  x
2.
4.
x  10  x  6  8
3x  1  5 x  1
still in problem:
A. Get
alone
B. Square each side again
4. Solve and check