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Ch 10.3 Solving Radical Equations

Ch 10.3 Solving Radical Equations. Objective: To solve equations involving square roots ( and equations involving perfect squares ). Definitions. Radical Equation: An equation involving the radical/square root symbol √ Extraneous Solution: A solution that is NOT valid.

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Ch 10.3 Solving Radical Equations

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  1. Ch10.3Solving Radical Equations Objective: To solve equations involving square roots (and equations involving perfect squares).

  2. Definitions Radical Equation: An equation involving the radical/square root symbol √ Extraneous Solution: A solution that is NOT valid

  3. Steps for Solvingradical (√) equations • Isolate the radical using the reverse order of operations. • Square both sides (the radical & the squared symbol cancel each other out) • Isolate the variable on one side & solve • Check your answers for extraneous solutions.

  4. Equations with Extraneous Solutions Note: The solution obtained by squaring both sides of the equation is not valid in the original equation. Check: Problem! An isolated radical cannot equal a negative! No solution

  5. Examples of Radical Equations 2) 1) 4) 3)

  6. More examples of Radical Equations 6) 5)

  7. Solve. Check for extraneous solutions. 7)

  8. Solve. Check for extraneous solutions. 8)

  9. Steps for SolvingSquared ( )² equations • Isolate the variable on one side. • If it is squared, take the square root (√) of both sides. • Add the +/- sign in front of one of the square root symbols (±√) For example: 2 + x² = 6 Step 1 -2 -2 x² = 4 Step 2 √x² = ±√4 x = ±2

  10. Solve the Rational Equations. Check for extraneous solutions. Solve. One Solution Two Solutions

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