Algebra 2
Chapter 6
Ms. Fisher
th
Thursday March 19
Agenda
Introduction: My name is Ms. Fisher and I will
be your Math teacher for the remainder of
the school year.
**Please frequently visit my website,
everything & anything you will need
is posted on there!
-My powerpoints, notes, answer keys, tutorials, textbook, etc…
Ms. Fisher’s Website
Agenda for today: Begin Ch 6
Teach lesson 6.1  Independent Work Time
Objective: To review and practice using the properties of exponents in preparation to
simplify expressions containing exponents.
Section 6.1- Simplifying Radical
Expressions
If n is odd,
If n is even
𝑛
𝑛
The nth root rule
𝑎𝑛 = a
𝑎𝑛 =
a
Example: 64 = +/- 8 (when n is even) b/c -8*-8 = 64 and 8 * 8=64
Principal root: |8| = 8
3
8 =2
can not be -2 bc
-2*-2*-2= -8
Principal root: Is the Positive root, You will be looking for the Principal root when n is
even!
Section 6.1- Simplifying Radical
Expressions
Simplify
4
16𝑎4 =
4
𝑎4 24 = |2a|
= 2|a|
2*2*2*2=16
(you have to put absolute value signs
around the variable a because you do not
know if a is positive)
3
27𝑎3 𝑏 6
=
3
33 𝑎3 (𝑏2 )3
= 3a𝑏 2
Section 6.1- Simplifying Radical Expressions
with cube roots
Steps Used to Simplify:
1. Factor expression under radicand into perfect squares,
cubes, or whatever is appropriate…
2. Use Multiplication Property to break into parts
𝑛
𝑛
𝑛
𝑎
𝑏
=
𝑎𝑏
3. Simplify
assume all variables are positive so no absolute values needed
EX:
75𝑎2 𝑏 3 = 52 3𝑎2 𝑏 2 𝑏
= 52 𝑎 2 𝑏 2
3𝑏 = 5ab 3𝑏
All perfect squares go here
All non-perfect squares
go here
6.1 Simplifying Expressions
3
Example:
=
24𝑥 4 𝑦 6
3
23
All Perfect cubes go here
∗
=
3
𝑥 3 (𝑦 2
)³
23 ∗ 3 ∗ 𝑥 3 ∗ 𝑥 ∗ (𝑦 2 )³
3
3x
All Non- Perfect cubes go here
Independent Work Time….
Begin your homework. Whatever you do not complete
in class you must finish at home. Remember, you can
access the textbook online from home!
Student Link to Textbook online
Username: Council Rock South1
Password: CouncilRockSouth1
Homework: Practice Form G #’s 13-32
Agenda: 6.2
Go over home – volunteers to board – Explain “Parking Lot”
Warm-up: Who can tell me the Multiplication Property?
𝑛
𝑎
𝑛
𝑛
𝑏
=
𝑎𝑏
Key component Need to have the same n
Teach Lesson 6.2
Independent Work Time
Objective: To use sums of perfect squares to solve a problem
6.2 Multiplying and Dividing Radical Expressions
Same index
To multiply radical expressions make sure they have the same n. Then use the
multiplication property to multiply factors into perfect squares, cubes
whatever the index is… Then simplify
Example:
12𝑎2 𝑏 3
*
3𝑎𝑏 2 c
=
(12𝑎2 𝑏 3 )(3𝑎𝑏 2 c)
=
36𝑎3 𝑏 5 c
*Remember when
multiplying, add the
exponents!
= 62 𝑎2 𝑎(𝑏²)2 𝑏 ∗ 𝑐
= 6²𝑎2 (𝑏²)2 * 𝑎𝑏𝑐
Perfect squares
simplest form
Non-Perfect squares
= 6ab² 𝑎𝑏𝑐
6.2 Multiplying Radical Expressions
Same index
To multiply radical expressions make sure they have the same n. Then use the
multiplication property to multiply factors into perfect squares, cubes
whatever the index is… Then simplify
Example:
3
9𝑥 5 𝑦 2
54
6𝑥𝑦 2 =
=
9
3 3
*
3
6
2
27 *2 =
3
=
3
3
(9𝑥 5 𝑦 2 )(6𝑥𝑦 2 )
54𝑥 6 𝑦 4
*Remember
𝑥 5 * x = 𝑥 5+1
𝑥6
3
33 2(𝑥²)3 𝑦 3 𝑦
3
3³(𝑥²)3 𝑦³ * ³ 2𝑦
Perfect cube
simplest form
*Remember (𝑥²)3
you multiply 2*3=6
Non-Perfect cube
= 3x²y * ³ 2𝑦
6.2 Dividing Radical Expressions
Property Dividing Radical Expression
If
𝑛
a
Example:
𝑛
b are real numbers and b≠ 0, then
24a2 𝑏³
=
𝑛
a =
𝑛
b
𝑛
a
𝑏
24a2 𝑏³
6𝑎𝑏
6𝑎𝑏
Step 1: Put under one square root sign
4𝑎𝑏²
2²𝑏²
𝑎
= 2b 𝑎
Step 2: Reduce a2−1=1 b3−1=2
Step3: Simplify; take all of our perfect squares &
factor them out
Step 4: Simplify
6.2 Dividing Radical Expressions
4y
−32𝑥
Example: ³ −32𝑥 4 y = ³
2
³ 2
Step 1: Put under one cube root sign
³ −16𝑥 4 y
³ −23 ∗ 2 ∗ 𝑥 3 ∗ x ∗y
³ −23 ∗ 𝑥 3
³ 2𝑥𝑦
= -2x ³ 2xy
Step 2: Reduce -16
Step3: Simplify; take all of our perfect cubes
& factor them out (cube bc index is 3)
Step 4: Simplify
6.2 Dividing Radical Expressions by rationalizing the denominator
A fraction should NOT have a radical in the denominator, if it does, you
need to rationalize the denominator.
𝑁𝑂
3𝑥
𝑦
What do you do? Look at the index.
Square root. Rewrite as a square root of a fraction, then get a
denominator that is a perfect square.
3𝑥𝑦
3𝑥 ∗ 𝑦
3𝑥 =
=
=
𝑦 ∗ 𝑦
𝑦²
𝑦
3𝑥𝑦
y
6.2 Dividing Radical Expressions by rationalizing the denominator
𝐼𝑓 the radical in the denominator is not a square root, the idea is the
same. You need to get a perfect square, cube, fourth, etc… in the
denominator to get rid of the radical in the denominator.
50𝑥
2𝑥
∗
5²
³ 2𝑥 = ³
=³
= ³ 50𝑥 = ³ 50𝑥
5³
5 ∗ 5²
³ 5³
5
³ 5
6.3 Adding & Subtracting Radical Expressions