Math 80 - Test 4 Review
(See Test 1-3 Reviews)
Chapter 7 – Radicals, Radical Functions, and Rational Exponents
7.1 Radical Expressions and Functions
Definition of the Principal Square Root; evaluating square roots; square root
functions;
finding the domain of a square root function; simplifying
; definition of the cube
root of a number; evaluating cube roots; cube root functions; simplifying
; definition
of the nth root of a number; evaluating nth roots; simplifying
7.2 Rational Exponents
Definition of rational exponents 
Properties
of Rational Exponents;
simplifying expressions with rational exponents using the properties of
exponents; using
rational exponents to simplify radical expressions.
7.3 Multiplying and Simplifying Radical Expressions
The Product Rule for Radicals; simplifying radicals by factoring; simplifying
when
n is even and a is nonnegative; multiplying and simplifying radicals.
7.4 Adding, Subtracting, and Dividing Radical
Expressions
Adding and subtracting radical expressions – combining like radicals;
adding/subtracting
radicals that first require simplification; The Quotient Rule for Radicals;
using the
quotient rule to simplify radicals; using the quotient rule to divide radical
expressions.
7.5 Multiplying with More Than One Term and
Rationalizing Denominators
Multiplying radicals with more than one term – using the distributive property,
the FOIL
method, and polynomial special product formulas to multiply radicals;
rationalizing
denominators containing one term; rationalizing denominators containing two
terms;
rationalizing numerators.
7.6 Radical Equations
Solving radical equations containing nth roots; solving an equation containing
two
radicals; applications of radical equations.
7.7 Complex Numbers
The imaginary unit, i; the square root of a negative number; complex numbers and
imaginary numbers; adding, subtracting, multiplying, and dividing complex
numbers; the
conjugate of a complex number; simplifying powers of i.
Review Problems
p. 557, Review Problems: 1-101
p. 559, Chapter 7 Test: 1-30