Leave all answers in reduced, radical form. No …teachers.sduhsd.net/dspragg/Algebra 1 Spring...
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Algebra 1: Chapter 10 Notes 1
1
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
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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
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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
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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
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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
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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
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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
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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