Algebra I: 1,001 Practice Problems For Dummies

Chapter 16

Reining in Radical and Absolute Value Equations

A radical equation contains at least one term that's a square root, cube root, or some other root. When solving radical equations, you apply a method that's effective but comes with a built-in error possibility; you may find (and need to recognize) extraneous solutions. You need to rewrite absolute value equations to solve them. The solutions of the rewrites are then the solutions of the original equation.

The Problems You'll Work On

Here's just a sampling of the radical things you work on in this chapter:

• Rewriting equations with only two terms and squaring both sides to solve
• Squaring both sides of an equation when starting with three terms
• Dealing with more than one radical term
• Catching extraneous solutions
• Graphing absolute value statements for clarity
• Solving absolute value equations after writing corresponding equations
• Checking for nonsense answers

What to Watch Out For

Here are a few things that may rock your boat, so be on the lookout:

• Squaring binomials correctly and not forgetting the middle term
• Factoring statements containing radicals correctly
• Checking for extraneous solutions by using the original equation, not the version changed in the process
• Catching impossible situations in initial absolute value equations

Solving Basic Radical Equations

686–689 Solve each radical equation by squaring both sides.

686.

687.

688.

689.

Checking for Extraneous Roots

690–697 Solve the radical equations by squaring ...