Algebra 1: Chapter 10 Notes 1

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Algebra Homework: Chapter 10 UPDATED ASSIGNMENT SHEET (Homework is listed by date assigned; homework is due the following class period)

Leave all answers in reduced, radical form. No decimals please!!! HW# Date In-Class Homework

24

M 5/19

Section 10.1: Simplifying and Multiplying

Radicals

HW#24 Pg. 489: 2-24 even Pg. 580: 41-48 all

25

T 5/20

Section 10.1: Dividing Radicals HW#25 Pg. 489: 15-23 odd, 28-50 even Watch Pythagorean Theorem Video

26 W

5/21 Section 10.2: The Pythagorean Theorem

HW#26 Pg. 496: 1-3, 7-9, 16-18

27

Th

5/22

Section 10.3: Adding, Subtracting, and

Distributing Radical Expressions

HW#27 Pg. 490: 33-51 odd Pg. 496: 10, 11, 20 Pg. 503: 1-3, 10-31x3

28 F

5/23

Section 10.4: Solving Radical Equations

HW#28 Pg. 510: 5, 11, 21, 26, 40, 54 (show checks on pg 510) HW 28 Worksheet (pg 20-21 in the notes packet)Print: Supplemental Unit Notes & Worksheets by Friday, 5/30

29 T

5/27 Section 10.4: Solving Radical Equations

HW #29: Pg. 506: 1-10 all Pg. 524: 1-8 all Pg. 510: 1-3, 9-12, 38, 45, 46 (Show ALL checks on pg. 510) Print: Supplemental Unit Notes & Worksheets by Friday, 5/30 Chapter 10 Test Thursday 5/29

30 W

5/28

Late Start Wednesday Chapter 10 Review

HW#30 Chapter 10 Study Guide (pg. 17-19 in the notes packet) Correct Study Guide in PEN using online key Chapter 10 Test Tomorrow Print: Supplemental Unit Notes & Worksheets

31 Th

5/29

Chapter 10 Test

HW#31 Pg. 580: 49-52, 55, 65-72 Print: Supplemental Unit Notes & Worksheets

Algebra 1: Chapter 10 Notes 2

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Notes #24: Real and Radical Expressions (Sections 10.1) A. Simplifying Square Roots Assume that all variables are nonnegative. (If it is a polynomial - ____________ first!!)

1.) 2m 2.)

216b 3.) 2(2 5)b

4.) 2 4 4x x 5.)

24 12 9d d

6.) 24 7.) 300 8.) 50m

9.) 248a 10.)

3125b 11.) 542g

Algebra 1: Chapter 10 Notes 3

3

12.) 7x 13.)

5( 5)m 14.) 25 10 5x x

15.) 48( 3)w 16.)

5200( 2)k 17.) 3 7150a b

B. Multiplying Square Roots

We will be multiplying expressions like: (2 20)(3 5) Steps: - simplify each radical completely

- (outside • outside) inside inside or ( )( ) ________a b c d - simplify your answer, if possible

*Remember, if you are multiplying polynomials, you must ________** Multiply and simplify, if possible:

18.) 5 6 19.) 7 7 20.) 64 7

Algebra 1: Chapter 10 Notes 4

4

21.) 4 x 22.) 2 3 4 6 23.) 2 2 5 10

24.) 33 6 4 8a a 25.)

3 55 12 -2 10x y xy 26.) 3 6 2 10x x

27.) 7 14a b 28.) 2

3 2 29.)2 3 3 212 3a b c a b c

30.) 2 3 3 415 20c d c d 31.)

2 32 10m n m n 32.) 2

5 7

Algebra 1: Chapter 10 Notes 5

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Notes #25: Dividing Radical Expressions (Section 10.1) Section 10.1: Dividing Rational Expressions

Examples:

9

16

12

27

Simplify:

1.) 81

100 2.)

121

196 3.)

25

144

4.) 6

24 5.)

75

300 6.)

320

80

a

a

7.)

3

5

8

2

m

m 8.)

4

3

24

3

x

x 9.)

7

3

60

3

y

y

Taking the square root of a fraction is the same as taking the square root of the ___________________

and ______________________ separately

OR

You can ___________ first and then split up the fraction

Algebra 1: Chapter 10 Notes 6

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However, sometimes our fractions don’t simplify as well…we end up with a radical expression in the denominator. This is NOT allowed!!

Ex:

24

30 Ex:

26

12

x

To fix this problem: - simplify the fraction as much as you can - multiply this simplified fraction (both ________ AND __________) by the exact term that is still in a square root sign on the denominator - simplify and reduce Simplify:

10.)

5

6 11.)

3

8

12.)

1

5 13.) 3

2

6

c

c

14.)

5

x 15.)

3

2x

Algebra 1: Chapter 10 Notes 7

7

16.)

12

2 17.)

3

27

d

18.)

14

3x 19.)

18

18

20.)

5108

2

xy

x

21.)

4

3

x

y

Algebra 1: Chapter 10 Notes 8

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Notes #26: Section 10.2: The Pythagorean Theorem Solve for x: 1.) 32 + 42 = x2 2.) 132 = 122 + x2 3.) x2 + 42 = 82 Right Triangles: Triangles with one _____________ ______________. hypotenuse = ____________________ legs = __________________________

Pythagorean Theorem:

( _________)2 + (_________)2 = (___________________)2 OR a2 + b2 = c2

Use Pythagorean Theorem to solve for the third side of each right triangle. Leave your answer in simplified radical form: 4.)

c

3

4

5.)

b

16

8

6.)

x x

6

7.)

x

4

2 3

Algebra 1: Chapter 10 Notes 9

9

8.) a = 5, b = 12, c = ?

9.) a = 1, c = 3 , b = ?

10.) A 15 foot ladder is leaning against a building. The bottom of the ladder is 9ft from the building. How high is the top of the ladder?

11.) How long must a wire be to reach from the top of a 12-m telephone pole to a point on the ground 5m from the foot of the pole?

Determine whether the given lengths can be sides of a right triangle. - use the longest length as c. Use the shorter two lengths as a and b - plug into the Pythagorean theorem: a2 + b2 = c2 - if both sides of the equation are equal, then the triangle is ________ If both sides of the equation are not equal, then the triangle is ______ _____________

12.) 2ft, 3ft, 4ft 13.) 6in, 7in, 8in 14.) 5cm, 5cm, 5 2 cm

Algebra 1: Chapter 10 Notes 10

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Notes #27: Other Operations on Radical Expressions (Section 10.3)

Adding and subtracting square roots is the same process as adding and subtracting ________________ ________________: look for ________________!!

Review: Add/Subtract 1.) 3x – 2y – 8x + 7y 2.) -2mn – (-3x2) + mn – 7x2 Steps for adding/subtracting radical expressions:

_______________ all radical expressions (break each term down as far as possible) Look for _________________ (underline, circle, box, etc) Combine like terms. Add the _______________, but leave the roots __________

Add/Subtract:

1.) 2 5 3 5 2.) 6 7 ( 3 7) 3.) 12 3 5 2

4.) 8 18 5.) 3 12 6 27

6.) 2 40 ( 3 90) 7.) 4x x

Algebra 1: Chapter 10 Notes 11

11

8.) 2 27 12 3 48x x 9.) 3 12 4 20 3 45 ( 2 300)

10.) 2 3 4 6 11.) 2 3 3 5 8 12.) 5 4 5

13.) 2 3 4 5 3 14.) 6 5 6 5 15.) 2

3 2 1

Steps for simplifying a fraction with a binomial in the denominator:

Multiply the _______ and ____________ of the fraction by the conjugate

Ex: 3

2 5 Ex:

2

3 5

Distribute in the numerator, use ________ in the denominator Reduce only if ________ terms can be simplified by the same factor

Ex: 3

2 5 Ex:

2

3 5

Algebra 1: Chapter 10 Notes 12

12

Simplify

1.) 8

4 6 2.)

6

10 2

3.) 13

7 5

4.) 15

8 5

Algebra 1: Chapter 10 Notes 13

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Notes #28 Review Concepts First: Solve for x 1.) 2 2 24 5x

2.) 2 2 24 8x

3.) 2 12x

Solving Radical Equations with Quadratics (Section 10.4) Solving Radical Equations:

Isolate the _________________ ______________ both sides. If one side is a binomial, be sure to use ___________ to square

it. Get all terms to one side to = 0 Solve the quadratic using: factoring, quadratic formula, or completing the square. Check your solution by ___________________ into the original equation. Check for

extraneous solutions.

1.) 2 3 1x

2.) 4 2 5x

3.) 2x x

4.) 35 2x x

Algebra 1: Chapter 10 Notes 14

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5.) 6 9x x 6.) 11 28x x

7.) 2 7 2x x 8.) 3 2 4x x

Algebra 1: Chapter 10 Notes 15

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Notes #29 Section 10.4: Solving Equations with radical expressions Steps for Solving Radical Equations:

Get the all alone Square ( )2 both sides (If you square a binomial, be sure to use _______!!) Solve for x Plug it back to check for extraneous solutions (you can never take the square root of a

______________ number)

Solve for x:

1.) 8x 2.) 1 3x

3.) 2 4 7x 4.) 1 2 5x x

Algebra 1: Chapter 10 Notes 16

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5.) 3 5 3x 6.) 21 5x x

7.) 2 5 3x 8.) 3 6 2 3m m

9.) 4 10 5 11x 10.) 22 8x x

Algebra 1: Chapter 10 Notes 17

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Algebra 1: Chapter 10 Study Guide Name: __________________ Simplify each radical expression.

1. 6 548x y 2. 3 7112m n 3. 56 72a a 4. 121

564

d

5. 8

6

49

64

y

x 6. 6 12 3 6 7. 23 2 2 10g g h h gh 8. 2

7 5

9. 48

81

b 10.

5 2

6m 11. 4

56

24

b

c 12. 5 11 6 11

Algebra 1: Chapter 10 Notes 18

18

13. 2 28 6 63 14. 3 32 7 8 15.

3

27

d

Solve for the variable: 16. a2 + 42 = 52 17. 52 + b2 = 102 18.

b15

9

Simplify:

19. 5 2 7 2 6 20. 4 3 2 2 5 3 2 21. 5 15 3 2

3

22. 6

3 2 23.

6

3 7

Algebra 1: Chapter 10 Notes 19

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Solve each radical equation and check your answer(s)

24. 2 75 2x x

25. 3 2 7x 26. 5 7 5x **NowgoonlinetocorrectyourworkinpenandprinttheSupplementalUnitNotesand

Worksheets**

Algebra 1: Chapter 10 Notes 20

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HW 28 Worksheet (2 pages) Name: Simplify each expression completely:

1.) 3 748a b 2.) 2 3 45 24x y x y 3.) 2 54 63m n mn

4.)26 12( 1)x 5.)

24 40 100y y

6.) 5 2 2 12 7.) 5 2 2 412 8 3 20j k j k jk jk

8.) 548

3

m

m 9.)

8

2 10.)

218

5

x

Algebra 1: Chapter 10 Notes 21

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11.) 3 2 6 2 12.) 2

5 6 13.) 1 3 2 4 3

14.) 21 7 15.) 5

12 2

16.) 7

5 3 17.) 3 7 3 18.) 12 5 27

19.) 4 5 125 40 20.) 3 18 6 72