Name
Class
Date
Reteaching 11-1
Simplifying Radicals
OBJECTIVE: Simplifying radicals involving
products and quotients
MATERIALS: None
The following are three examples of simplifying radicals. Simplifying each
radical makes it meet a condition that must be true to show that a radical
expression is in its simplest form.
Condition
Not in
Simplest Form
How to Simplify
Simplest Form
The Multiplication Property of Square Roots is used to simplify the radical.
The expression under
the radical sign has no
perfect square factors
other than 1.
"20
Rewrite as a product of
perfect squares and
other factors.
5 "4 ? 5
5 "4 ? "5
All rights reserved.
Example
2"5
The Division Property of Square Roots is used to simplify the radical.
16
Ä 25
The denominator
contains a radical
expression that is not a
perfect square
3
"2
Separate into two
radical expressions.
Simplify each separately.
"16
"25
Rationalize the
denominator by
multiplying the fraction
by a radical expression
equal to 1.
"2
5 3 ?
"2 "2
4
5
3"2
2
Exercises
Simplify each radical expression.
1. "2 ? "12
4. "3 ? "36
7. 2"28
10. "5
"64
8
2. 3"5 ? 2"5
3. 4"80
5. "18
6.
5
"3
8. 2 45
Ä
9.
14
Ä 25
11. 2 38
Ä
12.
16
Ä9
Lesson 11-1 Reteaching
Algebra 1 Chapter 11
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
The expression under
the radical sign is a
fraction.