Name___________________________
Hour_________
Ch. 11 Radicals Assignments
_____
Day 1:
Worksheet #1
_____
Day 2:
Worksheet #2
_____
Day 3:
Worksheet #3
_____
Day 4:
Worksheet #4
_____
Day 5:
Take Quiz 11–1
Worksheet #5
______
Day 6:
p. 590 (33-37) p. 595 (14-36 even)
_____
Day 7:
p. 601 (17-30) & p. 844 Lesson 11-2 (7, 14, 23)
_____
Day 8:
p. 601 (31-40) & p. 844 Lesson 11-2 (17, 18, 25)
_____
Day 9:
Quiz Review & Pythagorean Theorem Worksheet
_____
Day 10:
Take Quiz 11–2
p. 613 (13-19 odd, 33), p. 603 (70-72, bottom 6, 8)
p. 615 (48, 50, 51), & p. 621 (43, 46)
_____
Day 11:
Test Review Worksheet
_____
Day 12:
Take Chapter 11 Test
1
2
Day 1
Sec 11-1: Simplifying Radical
Expressions
Radical Expression: an expression that contains a square root.
Example:
40
Radicand: the expression under the radical sign.
The 
radicand is in simplest form if it contains no perfect squares.
Perfect Squares: a number squared.
Examples:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121…
Simplifying Radicals
2 18
27
2.
4.
96
5.
12
(reduce first)
3
6.
7.
9
same as
81
8.
80
9.
1
81
11.
 16
12.
18
98
10.

9
81
4
121
3.
425
1.
44
4
HW: Worksheet #1
3
Day 2
Multiplication and Division of Radicals
Rules for Multiplication:
1. a  b  ab
Rules for Division:
a
a
1.
=
b
b
2. No
can be left in a denominator.
Rationalize the denominator:
“what you do to the bottom you
have to do to the top”
Examples.
1.
2 6
2.
3.
3 2  5 10
4.
5.
5
5

8 12
6.
8  10
2 10
3 5
18
49
4
7.
9.
24
3 6
5
8
8.
10.
1
5
6
2
HW: Worksheet #2
5
Day 3
Square Roots of Variables
RULES:
Even powers:
Odd Powers:
Divide by 2.
Leave one and then divide by 2.
Evens:
1.
x2
2.
x4
3.
x6
4.
x8
5.
x1 0
6.
x3 6
x5
8.
x1 1
9.
x4 9
Odds:
7.
6
Simplify.
10.
4x2
11.
y1 2
12.
d6c4
13.
9x3
14.
5x4
15.
16a7
16.
50x 8 y 3
17.
2 6

3 8
HW: Worksheet #3
7
Day 4
Radical Review
Simplify.
1.
4
81
2.
6
36
3.
4.
5x 4
6
5.
5 3
2 6
6.
7.
a11b4
8.
72y5
9.
2 2
100
x7
2 36x 2 y 9
HW: Worksheet #4 ***Quiz Tomorrow!!!
8
Day 5
Sec 11-2: + and – Radical Expressions
Simplify.
1.
12x + 3 – 5x
2.
2 11 + 7 11 –
3
Combine Like Terms
* Add coefficients
*Radical stays the same
3.
6 5 –2 5 –5 5
5.
3 27 –
48
4.
7 2 + 8 11 – 4 11 –
6.
6 32 – 8 12 + 2 27
2
HW: Worksheet #5
9
Day 6
Multiply
1.
Products and Conjugates
2 ( 6 +4 8 )
2.
(4 5 –2 3 )(3 6 – 10 )
4.
(4 6  2 10 )(5 3  7 5 )
3.
(5  15 ) 2
5.
Find Perimeter and Area of the Rectangle.
Width:
4 3 –2 5
Length:
5 3 +7 5
Conjugates: rationalize the denominator with addition and subtraction of
radicals. Think Difference of Perfect Squares: (a + b)(a – b) = (a2 – b2)
Example:
(3  6 ) and (3  6 ) are conjugates.
1.
3
5 2
2.
5
7 5
3.
35  5 5
15
HW: p. 590 (33-37) p. 595 (14-36 even)
10
Day 7
Simplify.
1.
(5 3 )2
2.
(5 +
3 )2
Sec 11-3: Solving Radical Equations
Steps:
1.
Get radical with variable alone
2.
Square each side to get rid of
3.
4.
Solve
a. If only an x solve.
b. If x2 use factoring or quadratic formula.
Check all solutions (extraneous solutions)
Examples.
1.
2y  4
2.
2 x 6  8
3.
x 2 8
4.
x  5
5.
2x  16  0
6.
8
2x
5
11
HW: p. 601 (17-30) & p. 844 Lesson 11-2 (7, 14, 23)
11
Day 8
More Radical Equations
Steps:
1.
Get radical with variable alone
2.
Square each side to get rid of
3.
4.
Solve
a. If only an x solve.
b. If x2 use factoring or quadratic formula.
Check all solutions (extraneous solutions)
Solve and check.
1.
3.
x  x  20
3x  14  6  x
2.
5x2  4  2x
4.
10x2  9  3x
12
Application Problem
Tsunamis, or large tidal waves, are generated by undersea earthquakes in
the Pacific Ocean. The speed of the tsunami in meters per second is
s = 3.1 d , where d is the depth of the ocean in meter.
5.
Find the speed of the tsunami if the depth of the water is 10 meters.
6.
Find the depth of the water if a tsunami’s speed is 240 meters per
second.
HW: p. 601 (31-40) & p. 844 Lesson 11-2 (17, 18, 25)
13
Day 9
Practice for Quiz 11-2
Add or Subtract *Combine Like Terms
1.
12 + 27
Multiply
7 (5 + 2 3 )
2.
Solve
4.
*Get
3.
(5 +
2 )(7 + 3 2 )
by itself
5+2 x =9
14
Sec 11-4: Pythagorean Theorem
a
(leg)
c (hypotenuse)
a2 + b2 = c2
hypotenuse
b (leg)
1.
11
2.
a = 9, c = 15, b = ?
4.
a=
c
4
3.
a= 5
b = 10
c =?
5, b = 2 3, c = ?
5.
The measures of the sides of a triangle are 8, 11,
triangle?
40 . Is it a right
HW: Pythagorean Theorem WS & Quiz Review WS
***Quiz Tomorrow!
15
Day 10
Sec 11-5: Distance Formula
d=
(x2  x1 )2  (y2  y1 )2
Find the distance between each pair of points, round answers to the
nearest tenth.
1.
(1, 5), (3, 1)
2.
(3, –4), (–4, –4)
Find the missing coordinate, round answers to the nearest tenth.
3.
(2, -1) (a, 3) d = 5
4.
(5, a) (7, -3) d = 85
5.
An isosceles triangle has two sides of equal lengths. Determine
whether triangle ABC with vertices A(–3, 4), B(5, 2), and C(–1, –5) is
an isosceles triangle.
HW: p. 613 (13-19 odd, 33), p. 603 (70-72, bottom 6, 8)
p. 615 (48, 50, 51), & p. 621 (43, 46)
16