Page 303 - Algebra 1

L E S S O N Simplifying Expressions with Square Roots
46
and Higher-Order Roots
Warm Up
1. Vocabulary A is a number that is the square of an integer. (13)
Tell whether each number represents a perfect square. Justify your answer.
(13)
2. 25 3. 12 4. 49
Simplify.
(11)
5. 53
6. (-3)4
New Concepts A number has both a positive and a negative square root. The principal square root is the positive square root of a number. Typically, if no negative
sign is present, the principal square root is calculated.
Simplifying Expressions Using the Positive and Negative Values of the Square Root
Hint
Any positive number x has both a positive and negative square root. These can be written as ±√x .
Example
1
Simplify each expression.
a. √ 64 SOLUTION
2 √ 6 4 = √ 8
= √ 8 · 8 = 8
c. √ 0 SOLUTION
√ 0 = 0
e. √ -3 6 SOLUTION
b. - √ 9 SOLUTION
√ √ - 9=- 32
= - √ 3 · 3 = -3
_ d. √ 4
SOLUTION
√
=
√2 5
25
4 √ 4 __
25
22
=
√
= _2 5
_ √5
2
Online Connection www.SaxonMathResources.com
√- 3 6 has no real solution. There is no real number a such that a2 = -36.
288 Saxon Algebra 1