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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