## MTE 8 - Rational Exponents and Radicals at Danville Community College

### Course Description

Effective: 2012-01-01

Includes simplifying radical expressions, using rational exponents, solving radical equations and solving applications using radical equations. Credit is not applicable toward graduation.

Lecture 1 hour per week.

1 credits

### General Course Purpose

The purpose of this course is to develop competency necessary to succeed in 100-level math courses in solving applications using rational exponents and radical equations.

### Course Prerequisites/Corequisites

Prerequisites: MTE 7 or qualifying placement score.

### Course Objectives

- Demonstrate the equivalence of radical and rational exponent forms.
- Convert between square root and a1/2 forms.
- Convert between nth root and a1/n forms.
- Convert between combinations of nth root and mth power and am/n forms.
- Compute and estimate radicals.
- Calculate square roots via calculator.
- Estimate square roots.
- Calculate nth roots via calculator.
- Simplify radicals and radical expressions.
- Simplify using the properties of rational exponents.
- Simplify square roots.
- Simplify nth roots of variable expressions.
- Simplify radicals by using the multiplication property of radicals.
- Simplify radicals by using the division property of radicals.
- Perform operations (add, subtract, multiply) on radicals and radical expressions.
- Define like radicals.
- Combine and simplify like radicals.
- Multiply and simplify radicals.
- Rationalize the denominator (one term and two terms).
- Simplify radicals by rationalizing a denominator with one term.
- Simplify radicals by rationalizing a denominator with two terms.
- Solve radical equations.
- Define the imaginary unit and imaginary numbers.
- Define i = the square root of -1
- Define imaginary numbers
- Simplify square roots of negative numbers using the imaginary unit.
- Solve application problems involving radicals.
- Solve problems involving right triangles.
- Solve problems involving the Pythagorean Theorem.
- Solve problems involving the distance formula.

### Major Topics to be Included

- Demonstrating the equivalence of radical and rational exponent forms.
- Computing and estimating radicals.
- Simplifying radicals and radical expressions.
- Performing operations (add, subtract, multiply) on radicals and radical expressions.
- Rationalizing the denominator (one term and two terms).
- Solving radical equations.
- Defining the imaginary unit and imaginary numbers.
- Simplifying square roots of negative numbers using the imaginary unit.
- Solving application problems involving radicals.