Carson Elementary And Intermediate Algebra 3e

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Carson Elementary and Intermediate Algebra 3e
Section 10.1
Objectives
1.
Find the nth root of a number.
2.
Approximate roots using a calculator
3.
Evaluate radical functions
4.
Find the domain of radical functions
Vocabulary
n
?nth root
The number b is an nth root of a number a if b
= a.
Radicand
The number under the radical symbol.
Index
The number that indicates which root is to be used.
Prior Knowledge
Evaluating roots
Function – A relation in which every value in the domain (x) is paired with exactly one value in the range (y).
Domain – the set of all x values in a relation.
Function notation f(x). f is the name of the function and x is the variable.
Evaluating functions.
f(x) = 3x – 2
f(4) = 3(4) – 2 = 12 – 2 = 10
Solving linear inequalities. Remember to switch the direction of the inequality when both sides are multiplied
or divided by a negative number.
Interval notation and set builder notation.
x ≥ 5
[5, ∞) – Interval notation. Smallest possible number is written on the left.
{ x | x ≥ 5 } – set builder notation
New Concepts
Real numbers are divided into rational and irrational numbers. So far we have dealt exclusively with rational
(fraction) numbers. This chapter adds the irrational component. Radicals that can not be simplified to
rational numbers are irrational.
index
radical expression:
radicand
1. Evaluating nth roots.
4
 We CANNOT take an even root of a negative number.
4
or
16
.
 We CAN take an odd root of a negative number.
3
8
2
.
 If the index is even, there are 2 roots: one is positive, one is negative.
16
4
.
The positive number is the principle root.
The radical symbol represents the positive root.
V. Zabrocki 2011
page 1

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