**(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**