## MTE 8 - Rational Exponents and Radicals at Eastern Shore 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.

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