Algebra 2Chapter 6

Ms. Fisher

Thursday March 19th 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 The nth root rule If n is odd, = a If n is even = a

Example: = +/- 8 (when n is even) b/c -8*-8 = 64 and 8 * 8=64

= 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!

Principal root: |8| = 8

Section 6.1- Simplifying Radical Expressions Simplify = = |2a| = 2|a| (you have to put absolute value signs

around the variable a because you do not

know if a is positive)

= = 3a

2*2*2*2=16

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

= 3. Simplify assume all variables are positive so no absolute values neededEX: = = = 5ab All perfect squares go

here

All non-perfect squares go here

6.1 Simplifying Expressions

Example: = )³ = )³

All Perfect cubes go hereAll 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? = Key component Need to have the same nTeach Lesson 6.2Independent Work Time Objective: To use sums of perfect squares to solve a problem

6.2 Multiplying and Dividing Radical Expressions

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: * = )

=

=

= *

simplest form = 6ab²

Same index

*Remember when multiplying, add the exponents!

Perfect squares

Non-Perfect squares

6.2 Multiplying Radical Expressions

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: *= )

54 =

9 6 27 *2 =

3 3 2 3 = * ³

simplest form = 3x²y * ³

Same index

*Remember* x =

Perfect cube Non-Perfect cube

*Remember you multiply 2*3=6

6.2 Dividing Radical ExpressionsProperty Dividing Radical ExpressionIf are real numbers and b≠ 0, then =

Example: =

Step 1: Put under one square root sign

Step 2: Reduce

Step3: Simplify; take all of our perfect squares &

factor them out

= 2b Step 4: Simplify

6.2 Dividing Radical Expressions

Example: =

Step 1: Put under one cube root sign

Step 2: Reduce -16

Step3: Simplify; take all of our perfect cubes

& factor them out (cube bc index is 3)

= -2x Step 4: Simplify

6.2 Dividing Radical Expressions by rationalizing the denominatorA fraction should NOT have a radical in the denominator, if it does, you need to rationalize the denominator.

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. = = =

y

6.2 Dividing Radical Expressions by rationalizing the denominatorthe 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.

= = = = ³ √5 ³ √5³ 5

6.3 Adding & Subtracting Radical Expressions