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Chapter 16
Reining in Radical and Absolute Value Equations
Aradical 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.
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689.
Checking for Extraneous Roots
690–697 Solve the radical equations by squaring both sides; check for extraneous solutions.
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Squaring Both Sides of Equations Twice
698–701 Solve each radical equation by squaring both sides of the equation twice.
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Solving Radicals with Roots Other Than Square Roots
702–703 Solve the radical equations.
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703.
Solving Absolute Value Equations
704–713 Solve each absolute value