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Algebra 1: Chapter 10 Notes
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
24
M
5/19
Section 10.1: Simplifying and Multiplying
Radicals
25
T
5/20
Section 10.1: Dividing Radicals
26
W
5/21
Section 10.2: The Pythagorean Theorem
27
Th
5/22
28
29
F
5/23
T
5/27
30
W
5/28
31
Th
5/29
Section 10.3: Adding, Subtracting, and
Distributing Radical Expressions
Section 10.4: Solving Radical Equations
Section 10.4: Solving Radical Equations
Late Start Wednesday
Chapter 10 Review
Chapter 10 Test
Homework
HW#24
Pg. 489: 2-24 even
Pg. 580: 41-48 all
HW#25
Pg. 489: 15-23 odd, 28-50 even
Watch Pythagorean Theorem Video
HW#26
Pg. 496: 1-3, 7-9, 16-18
HW#27
Pg. 490: 33-51 odd
Pg. 496: 10, 11, 20
Pg. 503: 1-3, 10-31x3
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
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
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
HW#31
Pg. 580: 49-52, 55, 65-72
Print: Supplemental Unit Notes &
Worksheets
1
Algebra 1: Chapter 10 Notes
2
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.)
m2
16b 2
2.)
x2  4 x  4
4.)
3.)
5.)
6.)
24
7.)
9.)
48a 2
10.)
300
125b3
(2b  5) 2
4d 2  12d  9
8.)
11.)
50m
42g 5
2
Algebra 1: Chapter 10 Notes
12.)
15.)
x7
3
13.)
8( w  3) 4
( m  5)5
16.)
14.)
200(k  2)5
17.)
5 x 2  10 x  5
150a 3b 7
B. Multiplying Square Roots
We will be multiplying expressions like: (2
Steps: - simplify each radical completely
20)(3 5)
- (outside • outside) inside  inside or
- simplify your answer, if possible
( a b )(c d )  ________
*Remember, if you are multiplying polynomials, you must ________**
Multiply and simplify, if possible:
18.)
5
6
19.)
7 
7
20.)
64 
7
3
Algebra 1: Chapter 10 Notes
21.)
4 
22.) 2 3  4 6
x
24.) 3 6a  4 8a
3
27.)
30.)
7 a  14b
15c 2 d 3 
4
20c 3 d 4
25.) 5 12 x y  -2 10 xy
3
28.)

3 2
31.)

2
23.) 2 2  5 10
26.) 3 6 x  2 10 x
5
29.) 12a b c 
2 3
2m 2 n  10m3n
32.)
3a 3b 2 c
5 7 
2
4
Algebra 1: Chapter 10 Notes
Notes #25: Dividing Radical Expressions (Section 10.1)
5
Section 10.1: Dividing Rational Expressions
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
Examples:
9

16
12

27



Simplify:
1.)
4.)

81
100
6
24
2.)
121
196
3.)
5.)
75
300
20a 3
6.) 
80a
8m3
7.)
2 m5
3x3
25
144
60 y 7
24 x 4
8.)

9.)
3 y3
5
Algebra 1: Chapter 10 Notes
6
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:
6x2
12
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.)
12.)
14.)
5
6
11.)
1
5
5
x
13.)
15.)
3
8
2c
6c 3
3
2x
6
Algebra 1: Chapter 10 Notes
16.)
18.)
20.)
12
2
14
3x
108 xy 5

2x
7
17.)
19.)
d3
27
18
18
x4
21.)
y3
7
Algebra 1: Chapter 10 Notes
Notes #26: Section 10.2: The Pythagorean Theorem
8
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:
5.)
4.)
b
8
c
3
16
4
6.)
7.)
x
x
x
2 3
6
4
8
Algebra 1: Chapter 10 Notes
8.) a = 5, b = 12, c = ?
9
9.) a = 1, c =
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?
3,b=?
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
9
Algebra 1: Chapter 10 Notes
Notes #27: Other Operations on Radical Expressions (Section 10.3)
10
Adding and subtracting square roots is the same process as adding and subtracting ________________
________________: look for ________________!!
Review: Add/Subtract
2.) -2mn – (-3x2) + mn – 7x2
1.) 3x – 2y – 8x + 7y
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
4.)
8  18
6.)
2 40  (3 90)
2.)
 6 7  ( 3 7 )
5.)
7.)
3.)
12 3  5 2
3 12  6 27
x  4x
10
Algebra 1: Chapter 10 Notes
11
7 12 x2  3 48x2
8.)
10.)
13.)

2 3 4 6

 2  3  4  5 3 
9.)
11.) 2 3
14.)

3 12  4 20  3 45  ( 2 300)
3 5 8

 6  5  6  5 

5 4 5
12.)


15.) 3 2  1

2
Steps for simplifying a fraction with a binomial in the denominator:

Multiply the _______ and ____________ of the fraction by the conjugate
3
2
Ex:
Ex:
2 5
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
11
Algebra 1: Chapter 10 Notes
12
Simplify
1.)
3.)
8
4 6
13
7 5
2.)
6
10  2
4.)
15
8 5
12
Algebra 1: Chapter 10 Notes
Notes #28
Review Concepts First: Solve for x
1.) x 2  42  52
2.) x 2  42  82
13
3.) x 2  12
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 x  3  1
2.) 4  x  2  5
3.)
x2  x
4.)
35  2x  x
13
Algebra 1: Chapter 10 Notes
5.) 6 x  9  x
7.)
2x  7  x  2
14
6.)
11x  28  x
8.)
3x  2  4  x
14
15
Algebra 1: Chapter 10 Notes
Notes #29 Section 10.4: Solving Equations with radical expressions
Steps for Solving Radical Equations:
 Get the
all alone
2
 Square ( ) 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.)
3.)
x 8
2x  4  7
2.)
x 1  3
4.)
x 1  2x  5
15
16
Algebra 1: Chapter 10 Notes
5.)
3x  5  3
6.)
7.)
x 2 5  3
8.)
3m  6  2m  3
10.)
x  2  x2  8
9.) 4  10  5 x  11
x 1  x2  5
16
17
Name: __________________
Algebra 1: Chapter 10 Notes
Algebra 1: Chapter 10 Study Guide
Simplify each radical expression.
1.
48x 6 y 5
5.
49 y 8
64 x 6
6.
9.
48b
81
10.
2.
112m3 n 7
6 12  3 6
5 2
6m
3. 6a 72a 5
4. 5d
7. 3g 2 g 2 h  2h 10 gh
11.
56b
24c 4
8.
12.
121
64
7 5 

2
5 11  6 11

17
18
Algebra 1: Chapter 10 Notes

14. 3 32  7 8
13. 2 28  6 63
Solve for the variable:
16. a2 + 42 = 52
17. 52 + b2 = 102

15.
d3
27
18.
15
b
9
Simplify:

19. 5 2 7  2 6
22.
6
32

20.
4

32 2 5 3 2
23.

21.
5 15  3 2
3
6
3 7
18
Algebra 1: Chapter 10 Notes
Solve each radical equation and check your answer(s)
24.
x 2  75  2 x
25.
x3  2  7
19
26. 5  7  x  5
**NowgoonlinetocorrectyourworkinpenandprinttheSupplementalUnitNotesand
Worksheets**
19
20
Algebra 1: Chapter 10 Notes
Name:
HW 28 Worksheet (2 pages)
Simplify each expression completely:
1.)
48a 3b 7
4.) 6
12( x  1)2
6.)
8.)
2.) 5 x 2 y 24 x 3 y 4
48m5
3m
4 y 2  40 y  100
5.)

 5 2  2 12 
7.) 12 j 5 k 8 j 2 k
9.)
8
2
3.) 4m 2 n 63mn 5
 3 jk
2
10.)
20 jk 4

18 x 2
5
20
Algebra 1: Chapter 10 Notes

11.) 3 2 6  2

14.) 1  7
16.)



12.) 5 6

2
7
5 3
19.) 4 5  125  40

2

13.) 1  3 2  4 3
15.)
17.)
21

5
12  2
37 3
18.)

12  5 27

20.) 3 18  6 72
21