Do Now 5/4/10Do Now 5/4/10Take out HW from last night.Take out HW from last night.

Cumulative Test Chapters 1-10Cumulative Test Chapters 1-10

Copy HW in your planner.Copy HW in your planner.Text p. 723, #4-52 multiples of 4, #67 & 68Text p. 723, #4-52 multiples of 4, #67 & 68

In your notebook, define a perfect square in In your notebook, define a perfect square in your own words. Then list the squares of the your own words. Then list the squares of the numbers 1 to 20. numbers 1 to 20. (remember this?)(remember this?)

ClassworkClassworkText p. 708, #1-16 all; not 3Text p. 708, #1-16 all; not 3

1) radicand1) radicand 2) square root2) square root 4) 94) 9 5) -85) -8 6) 6) ±10±10 7) -117) -11 8) 4y – 128) 4y – 12

9) 2x – 49) 2x – 4 10) –x² - 11x10) –x² - 11x 11) 4x11) 4x² - 36x² - 36x 12) (x + 2)²12) (x + 2)² 13) (m + 8)(m + 1)13) (m + 8)(m + 1) 14) (r + 7)( r + 1)14) (r + 7)( r + 1) 15) (b + 8)(b + 2)15) (b + 8)(b + 2)

Chapter 11 Chapter 11 “Radical and Geometry Connections”“Radical and Geometry Connections”

(11.2) (11.2) Simplify Radical ExpressionsSimplify Radical Expressions (11.3)(11.3) Solve Radical EquationsSolve Radical Equations (11.4) (11.4) Apply the Pythagorean TheoremApply the Pythagorean Theorem (11.5) (11.5) Apply the Distance and Midpoint FormulasApply the Distance and Midpoint Formulas

ObjectiveObjectiveSWBAT simplify radical expressionsSWBAT simplify radical expressions

Section 11.2 “Simplify Radical Expressions”Section 11.2 “Simplify Radical Expressions”

A radical expression is in A radical expression is in simplest formsimplest form if the following conditions are true: if the following conditions are true:

-No perfect square factors other thanNo perfect square factors other than 1 are in the radicand.1 are in the radicand.

-No fractions are in the radicand.-No fractions are in the radicand.

-No radicals appear in No radicals appear in the the denominator of a denominator of a fraction.fraction.

Product Property of RadicalsProduct Property of Radicals

The square root of a product equals the The square root of a product equals the product of the square roots of the factors. product of the square roots of the factors.

baab

9218 2332

xx 44 xx 22

31648 3434

Try It Out…Try It Out…

32

24

24

216

39x

xx

xx

2

2

9

9

xx 43

234

34

x

xx

xxy 37 2

xxxx 33 When multiplying radicals, multiply the radicands together and multiply When multiplying radicals, multiply the radicands together and multiply the numbers in front of the radical sign together. Then simplify.the numbers in front of the radical sign together. Then simplify.

34

34 2

x

x

22

2

73

73

yx

xxy

73

73 22

xy

yx

Quotient Property of RadicalsQuotient Property of RadicalsThe square root of a quotient equals the The square root of a quotient equals the

quotient of the square roots of the quotient of the square roots of the numerator and denominator. numerator and denominator.

b

a

b

a

5

4

25

16

25

16

9

21

81

21

81

21

Try It Out…Try It Out…

100

13

100

13

100

13

10

13

2

7

x

22

77

xx

x

7

Rationalizing the DenominatorRationalizing the DenominatorWhenever there is a radical (that is not a Whenever there is a radical (that is not a

perfect square) in the denominator, the perfect square) in the denominator, the radical must be eliminated by radical must be eliminated by rationalizing rationalizing the denominator.the denominator.

7

5

7

7

49

75

7

75

Need to Need to rationalize therationalize thedenominatordenominator

Multiply by 1Multiply by 1 Product property Product property of radicalsof radicals

SimplifySimplify

Try It Out…Try It Out…

b3

2

b

b

b 3

3

3

2

b

b

b

b

3

6

9

62

6

7

6

6

6

7

6

67

Need to Need to rationalize therationalize thedenominatordenominator

Multiply by 1Multiply by 1

SimplifySimplify

Adding and Subtract RadicalsAdding and Subtract RadicalsYou can add and subtract radicals that You can add and subtract radicals that

have the same radicands. have the same radicands.

109132104

4835

105132

31635

Think of as combining ‘like terms’Think of as combining ‘like terms’

Look for common radicandsLook for common radicands

SimplifySimplify

3435

39

Try It Out…Try It Out…

253622

3627

2329

22169

2249

237

2236

Multiplying Radical ExpressionsMultiplying Radical Expressions You can multiply radical expressions the same way you You can multiply radical expressions the same way you

multiplied monomials and binomials using the distributive multiplied monomials and binomials using the distributive

property and FOIL.property and FOIL.

54 100

1054

)204(5

49 143 14 43

1421

61427

simplify & combine like termssimplify & combine like terms

)237)(27(

Try It Out…Try It Out…

187 66

66221

66927

)637(6

20 24 25 4

218 simplify & combine like termssimplify & combine like terms

)25)(24(

HomeworkHomework Text p. 723, #4-52 multiples of 4, Text p. 723, #4-52 multiples of 4,

#67 & 68#67 & 68