Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
Algebra II / E&I Algebra
Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III
Sequences and Infinite Series Power Series Vectors and Geometry of Space Vector-Valued Functions
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
Course: Algebra III / Intermediate Algebra
Topic: Nonlinear Equations and Applications

Overview

Today we will transition from radical expressions to radical equations. We will now be able to solve equations that contain a radical (or two!) for x. The process involves eliminating the radical and solving the resulting equation. You eliminate the radical by isolating it and squaring (or cubing, fourthing, etc.) both sides of the equation.

CAUTION: Be sure to square (or cube, etc.) the entire side of the equation not individual terms. I.e., squaring both sides of √(x) = √(y)+2 does not make x=y+4. Actually it makes x = (√(y)+2)2 = (√(y)+2)(√(y)+2) which must then by FOILed.

CAUTION: You must always check your answers when you even-power both sides due to the potential for extraneous solutions. Check by plugging each answer back into the original equation. Then simplify each side to see if they match (and don't power each side to eliminate the radical as that is where the potential error can enter in the first place!).

CAUTION: Recall that an even root can never be equal to a negative number, so something like √(x-5) = -3 is automatically no solution. Don't waste your time trying to solve it.

You should be able to solve more complicated radical equations graphically. See the supplemental resources below for assistance.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 11.1.1 Solve radical equations algebraically that contain:
a single radical (any index), or fractional exponents, or two square roots
• 11.1.2 Recognize extraneous solutions to radical equations
• 11.1.3 Determine the number of solutions a radical equation will have by graphing the equation
• 11.1.4 Solve a radical equation by graphing electronically

Terminology