Intermediate Algebra Exam 4 Information
Good evening! Information about the fourth exam is listed below. Let me know if you have any questions
about the material.
Thanks,
Chad
Exam 4 Info:
20 problems + 4 bonus questions (pick one)
Concepts:
Finding/Evaluating nth Roots
Working with Rational Exponents
-The 'old' exponent rules were for integer powers only. In this chapter, the rules have been extended
to include rational powers (see page 466 for a nice summary).
Radical Arithmetic
-Multiplying and dividing radicals (apply the Product Rule for Radicals or the Quotient Rule for
Radicals)
-Adding and subtracting radicals (in order to add or subtract, we need like terms)
Simplifying Radicals
-A radical expression is in simplest form if three conditions are satisfied:
1. there are no factors in the radicand raised to powers greater than or equal to the root index
2. there are no fractions in the radicand
3. there are no radicals in the denominator of the radical expression
Rationalizing the Denominators of Radical Expressions
Solving Radical Equations (procedure is outlined on page 500)
-Isolate the radical, raise both sides of the equation to the power equal to the root index, and then
solve the resulting equation. This process may lead to extraneous solutions, so it's always a good
idea to make sure your possible solutions actually satisfy the original radical equation.
Complex Numbers
-Adding and subtracting complex numbers (combine like terms -> reals with reals, imaginaries with
imaginaries)
-Multiplying complex numbers (remember that i^2 = -1)
-Dividing complex numbers (process is similar to rationalizing the denominator of a radical
expression)
Good practice problems:
Ch. 8 Review p. 516: #13-91 odd, 97-121 odd