Page 413 - Algebra 1

L E S S O N Simplifying Radical Expressions 61
Warm Up
1. Vocabulary The __________ of x is the number whose square is x. (13)
Simplify. 2. √ 36
(13)
3. √ 81 (13)
4. √ 1 _
(46) 4
5. √ 54 is between which two consecutive integers?
(13)
New Concepts A radical expression is an expression containing a radical. Radical expressions can be simplified using the Product of Radicals Rule.
Product Property of Radicals
If a and b are non-negative real numbers, then √a √ b = √ ab and √ ab = √a √ b.
Factoring a radicand into perfect squares is one way to determine if a radical expression can be simplified.
Simplifying With Perfect Squares
Simplify using perfect squares.
Example
1
Math Language
A perfect square is a number that is the square of an integer.
Online Connection www.SaxonMathResources.com
a. √ 22 5 SOLUTION
√2 2 5
= √ 9 · 2 5 = √ 9 · √ 2 5 =3·5
= 15
b. √ 72 SOLUTION
√7 2
= √ 9 · 4 · 2
= √9 · √4 · √2 = 3 · 2 √ 2
= 6 √ 2
Find the perfect squares that are factors of 225. Product of Radicals Rule
Simplify the perfect squares.
Multiply.
Find the perfect squares that are factors of 72. Product of Radicals Rule
Simplify.
Multiply.
398 Saxon Algebra 1