Simplifying Radicals
0Notes and Practice Problems
Guided Notes and Practice
Begin with necessary prerequisite skills
and then go through examples of
simplifying radicals. Includes square
roots with variables and rationalizing
the denominator (with and without
conjugates).
CCSS Alignment
8.EE.A.2
HSN.RN.A.2
Teacher Guide
Unit
Concepts
Radicals
Students will:
• Simplify radicals (square roots only)
Common Core
Standards
8.EE.A.2
HSN.RN.A.2
Suggested Use
Start by reviewing the prerequisite skills. Then go through
the examples with students, emphasizing the key
concepts involved. Each example corresponds with a
guided practice problem. After the lesson, check for
understanding by having students complete the 10
practice problems at the end.
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Radicals
Name___________________
Date_______Class_________
Notes: Simplifying Radicals
Objective:
Prerequisite Skills
Prime Factorization
28
84
18
120
Example 1: Multiplying Square Roots
2( 8
2 3 ( 3 4 ( 12
5( 5
Example 2: Simplifying Radicals
90
120
210
Square Roots
List all of the perfect squares from 1-100:
Place the following values on the number line
provided:
4
10
9
12
24
20
Key Concepts
𝑥 ( 𝑦 = 𝑥𝑦
𝑥
/
Guided Practice
2 ( 18
2 5 ( 10 ( 2 2
=𝑥
if 𝑥 ≥ 0
Key Concepts
Is it simplified?
ü No radicands have
perfect square factors
(other than 1)
ü No radicands in the
denominator
ü Radicands are integers
6
/
Guided Practice
84
54
180
© Applicable Algebra, 2017
Example 3: Simplifying Square Roots
with Variables
Key Concepts
𝑥/
Guided Practice
𝑎4
𝑥(𝑥 =𝑥
9𝑥 / 𝑦 2
𝑦(𝑦(𝑦(𝑦 =𝑦
20𝑥 3 𝑦 4 𝑧 6
64𝑎2 𝑏9:
50𝑎; 𝑏 / 𝑐99
𝑧(𝑧(𝑧 =𝑧 𝑧
Example 4: Rationalizing the
Denominator
2
/
Key Concepts
Is it simplified?
Guided Practice
5
7
25
20
ü No radicands have
perfect square factors
(other than 1)
ü No radicands in the
denominator
ü Radicands are integers
𝑥
Conjugates
𝑎
6
𝑎 𝑏+𝑐 𝑑
18
36
40
24
and
𝑎 𝑏−𝑐 𝑑
2
5+ 3
5
4+ 7
3 + 11
and
3 − 11
Practice Problems
Simplify each expression.
1. 24
2. 3 36
3. 6 ( 10
6. 50𝑎3 𝑏 4
7. 3 25𝑥 /
8.
32
9/
4. 2 7 ( 3 7
9.
94
3
5. 16𝑥 2
10.
2
4B 3
© Applicable Algebra, 2017
Raf,icals
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Name
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Date
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Prerequisite $kills
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Place the following values on the number line
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z,l5 . z,l4
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List all of the perfect squares from L-loo:
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alrcadt sirnPl ifr<d
vzi-o
/
/
No radicands have
perfect square factors
(other than r)
No radicands in the
denominator
Radicands are integers
=\6!
= Qt
Guided Praclice
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x
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'6
Guided plaotice
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= pffi
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Applicable Algebra, 2017
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No radicands have
perfect square factors
(other than r)
/ No radicands in the
denominator
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Co4,W4atr ,
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21+18
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Applicable Algebra, 2017
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