Download U1 W3 L1 Simplify Radicals

Unit 1 Relationships Between
Quantities and Expressions
Week 2
Lesson 1 – Simplify Radicals
(restricted to square roots only)
Today’s Objective
• MGSE9-12.N.RN.2 Rewrite expressions involving
radicals (restricted to square roots only)
• MGSE9-12.N.RN.3 Explain why the sum or product of
rational numbers is rational; why the sum of a
rational number and an irrational number is
irrational; and why the product of a nonzero rational
number and an irrational number is irrational.
• Objective: Students will simplify radical
expressions
Essential Questions
• What do you already know about square
roots?
• What is a perfect square?
• What is rational number?
• What is a irrational number?
Vocabulary
•
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•
•
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Simplify
Like Terms
Radicals
Radicands
Simplest Form
Factors
Rational Numbers
Irrational Numbers
Read, Write, Draw, Solve
Isaiah says that
is an irrational number
because it is a radical number. Do you agree or
disagree, explain why.
Perfect Squares
The square of whole
numbers.
1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 ,
121, 144 , 169 , 196 , 225, etc
Square Root Of A Number
2
Recall: If b = a, then b is a square root of a.
2
Example: If 4 = 16, then 4 is a square root
of 16
What is a square root of 25? 64? 100?
5
8
10
Positive Square Root
Negative Square Root
Positive & Negative
Square Root
Is there a difference between
&
?
Which expression has no real
roots?
Evaluate the expression
is not real
The expression equal to
is equivalent
to a positive integer when b is
A.
B.
C.
D.
-10
64
16
4
You know how to find the square root
of a perfect square.
What happens if the number is not a
perfect square?
Does it have a square root?
What would the square root look like?
Numbers with a Root
Radical numbers are typically irrational numbers
(unless they simplify to a rational number). Our
calculator gives:
2 1.41421
But the decimal will go on forever and not repeat
because it is an irrational number. For the exact
answer just use:
2
Some radicals can be simplified similar to simplifying a
fraction.
Rational/Irrational Numbers
• Review Game
• Practice with Rational/Irrational Numbers
What happens when the radicand is not a
perfect square?
Rewrite the radicand as a product of its
largest perfect square factor.
Simplify the square root of the perfect
square.
When simplified form still contains a
radical, it is said to be irrational.
Try These.
Identifying the largest perfect square factor when simplifying radicals
will result in the least amount of work.
Ex:
Not simplified! Keep going!
Finding the largest perfect square factor results in less work:
Note that the answers are the same for both solution processes
Simplify
A
B
C
D
already in simplified form
Simplify
A
B
C
D
already in simplified form
Simplify
A
B
C
D
already in simplified form
Simplify
A
B
C
D
already in simplified form
Simplify
A
B
C
D
already in simplified form
Note - If a radical begins with a coefficient before
the radicand is simplified, any perfect square that
is simplified will be multiplied by the existing
coefficient. (multiply the outside)
Express
in simplest radical form.
Simplify
A
B
C
D
Simplify
A
B
C
D
Simplify
A
B
C
D
Simplify
A
B
C
D
Simplify
A
B
C
D
A
20
B
10
C
7
D
4
Exit Ticket
A
6
B
2
C
3
D
8
Online Practice
• Click on the link below and complete the
practice
– For the True/False questions (1-3) you must
provide an explanation for your choice.
– For problems 1-8 you must show work
• Practice Simplifying Radicals