Warm­Up
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10.1 Simplifying Radical Expressions
Objective ­
To be able to simplify radical expressions.
Vocabulary
Radical Expression ­ An expression that contains a square root
Radicand ­ the expression under the radical sign
1
Simplest Radical Form
A radical expression is in simplest form when the following three conditions have been met.
3
1
No radicands have perfect square factors other than 1
2
No radicands contain fractions
No radicals appear in the denominator of a fraction
2
List of Perfect Squares
Square Root Perfect Square
Square Root Perfect Square
1
1
9
81
2
4
10
100
3
9
11
121
4
16
12
144
5
25
13
169
6
36
14
196
7
49
15
225
8
64
16
256
3
Square Root Properties
Product Property of Square Roots
Quotient Property of Square Roots
4
Simplify
1)
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
2)
5
Simplify
3)
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
4)
6
Simplify
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
5)
6)
7)
8)
7
Simplify
9)
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
10)
8
Simplify
11)
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
12)
9
Rationalizing the Denominator
A method used to eliminate radicals from a denominator
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
Simplify
14)
13)
10
Simplify
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
15)
11