Name____________________________________________________Date___________________Hour_1st__
COMPLETED ASSIGNMENTS
1.
2.
1
2
3
4
5
6
7
EC
INCOMPLETE ASSIGNMENTS
Complete assignments = all
questions done OR questions
tried
Tried question = original question
written down, a visual attempt,
AND explanation of difficulty or
question you had
1.
2.
3.
All incomplete questions
numbers need to written on the
white board before the bell
Incomplete hwk = hwk club =
full credit (must have signature)
if competed
Incomplete homework is ONLY
accepted the following day for
credit
Assignment
Section
Date
11.1
4/8
p. 581: 1-27
11.1
4/9
p. 581: 28-51
11.4
4/10
p.603: 1-25 Odd
11.4
4/11
Activity Finish,
p.603: 2-26 E, 28-33 all
11.5
4/12
p.610 1-29 EOO,
4/15
Review 4C
4/16
Quiz 4C
Radical Equations Wks
Total Points
Unit 4C – Exponential Functions (Day 1)
POINTS
1.
Points for fixed assignments
decrease by 1 for every fixed
assignment
a. 1 fix = 4pts
b. 2 fix = 3pts ea
c. 3 fix = 2pts ea
d. 4 + = 1pt ea
5 Pts
Fix/HC
0
Lesson 11.1: Simplifying Radicals
Multiplication Property of Square Roots
For every number a  0 and b  0 , ab  a  b .
Examples:
54  9  6
75  25  3
Examples: Removing Perfect Square Roots
1. Simplify each radical expression.
a. 192
d.  5 300
Variables and Exponents


A variable with an even exponent is a perfect square
An odd variable is the product of a perfect square and the variable
EX:

n 3  n 2  n , so
n3  n 2  n
Assume that all variables of all radicands represent nonnegative numbers.
Example: Removing Variable Factors
2. Simplify each radical expression.
a.
45a 5
c.  a 60a 7
b.
27n 2
d.
x2 y5
USING THE MULTIPLICATION PROPERY OF SQUARE ROOTS IN REVERSE
Examples: Multiplying Two Radicals
3. Simplify each radical expression.
a. 8  12
c. 5 3c  6c
Hwk Alg 1; p. 581: 1-27
b.
13  52
d. 2 5a 2  6 10a 3
Unit 4C – Exponential Functions (Day 2)
Lesson 11.1: Simplifying Radicals
You can use the Division Property of Square Roots to simplify expressions.
Division Property of Square Roots
a
a

For every number a  0 and b  0 ,
.
b
b
16
16 4


25
25 5
Example:
Examples: Simplifying Fractions Within Radicals
1. Simplify each radical expression.
11
a.
49
25 p 3
q2
c.
b.
144
9
d.
75
16t 2
Examples: Simplifying Radicals By Dividing

When the denominator of the radicand is not a perfect square, it may be easier to divide first and then simplify the radical
expression.
2. Simplify each radical expression.
a.
𝟑𝒙𝟑
𝟐𝟓
√
b. √𝟐𝟏𝒙
𝟓
Rationalizing a Denominator

If a radicand in the denominator of a radical expression is not a perfect square you simplify by ____________ the
denominator

Rationalizing = Multiplying both the numerator and denominator by the same radical expression. Choose a radical
expression that will make the denominator a perfect square (usually by itself)
a.
𝟐
√𝟓
b.
√𝟕
√𝟖𝒏
Hwk: Alg 1; p. 581: 28-51
Unit 4C – Exponential Functions
Lesson 11.4: Operations with Radical Expressions
For radical expressions, like radicals have the same radicand. Unlike radicals do not have the same radicand.
For example, 4 7 and -12 7 are like radicals, but 3 11 and 2 5 are unlike radicals.
To simplify sums and differences, you use the Distributive Property to combine like radicals.
Examples: Combining Like Radicals
1. Simplify each expression.
a. 2  3 2
b.  3 5  4 5
Examples: Simplifying to Combine Like Radicals
You may need to simplify a radical expression to determine if you have like radicals.
2. Simplify each expression.
a. 7 3  12
b. 3 20  2 5
Examples: Using the Distributive Property
3. Simplify each radical expression.
a. 5 (2  10 )
b. 2x ( 6x  11)
Example: Simplifying Using FOIL
If both radical expressions have two terms, you can multiply the same way you find the product of two
binomials, by using FOIL.
4. Simplify each radical expression.
a. ( 5  2 15)( 5  15)
Examples: Rationalizing a Denominator Using Conjugates
5  2 and
5  2 are conjugates. The product of two conjugates results in a difference of two squares.
Conjugates are the sum and the difference of the same two terms. The radical expressions
( 5  2 )( 5  2 ) 
Notice that the product of these conjugates has no radical.
You may recall that a simplified radical expression has no radical in the denominator. When a denominator
contains a sum or difference including radical expressions, you can rationalize the denominator by multiplying
the numerator and the denominator by the conjugate of the denominator. For example, to simplify a radical
5 2
6
expression like
, you multiply by
.
5 2
5 2
5. Simplify each expression.
6
a.
5 2
Hwk: Alg 1; p.603: 1-25 O
b.
4
7 5
1 = 1
14 
2 
15 
3 
16 = 4
4 = 2
17 
5 
18 = 9∙2 = 32
6 
19 
7 
20 = 5∙4 = 25
8 
25 = 5
9 = 3
36 = 6
10 
49 = 7
11 
64 = 8
12 = 4∙3 = 23
81 = 9
13 
100 = 10
__________________________________________________________________________________________
Amusement Park Activity
1. Design your park
a. Include at least three rides with a drop and a loop (name the rides and your park).
On a roller coaster ride, your speed in a loop depends on the height of the hill you have just come down and the
radius of the loop in feet.
The equation v  h  2r gives the velocity v in feet per second of a car at the top of the loop.
2. Scenario
a radius of 18 ft. You want the car to have a
velocity of 30 ft/s at the top of the loop.
b. Suppose the loop on another ride has a radius of
24 ft. You want the car to have a velocity of 35 ft/s
at the top of the loop.
3. Guess how high the hill should be
3. Guess how high the hill should be
4. Calculate (Show all work)
4. Calculate (Show all work)
a. Suppose the loop on one of your parks rides has
5. Create your own scenario modeling one of the rides from your amusement park (loop
radius and velocity) and calculate how high the hill should be.
Unit 4C – Exponential Functions
Lesson 11.5: Solving Radical Expressions
DEFINITION
A _________________________ is an equation that has a variable in a radicand. You can often solve a radical equation by getting
the radical by itself on one side of the equation. Then you square both sides.

Remember that the expression under a radical must be nonnegative
Solving with radicals (Solve twice)
1.
2.
3.
Solve for the radical
Remove the radical (use the inverse: exponential)
Solve for the variable
Examples: Solving by Isolating the Radical
1. Solve each equation. Check your solution.
a. x  3  4
c.
a  4  12
b.
x  7  12
d.
c2 6
Examples: Solving With Radical Expressions on Both Sides
* You can square both sides of an equation to solve an equation involving radical expressions
3. Solve the radical equations.
a. 3n  2  n  6
b.
3t  4  5t  6 . Check your answer.
Examples: Identifying Extraneous Solutions
NOTE
When you solve an equation by squaring each side, you create a new equation. This new equation may have solutions that do not
solve the original equation. (Recall the ± ?)
**Check your answers for extraneous solutions
4. Solve x  x  6 .
4.b. Solve y 
y  2 . Check your solutions.
Examples: No Solution
It is possible that the only solution you get after squaring both sides of an equation is extraneous. In that case,
the original equation has no solution.
5. Solve
2x  6  4 .
Hwk Alg1: p.610 1-29 EOO,
5.a. Solve 8  2n  20 . Check your solutions.