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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

Steps for Solving radical (√) equations 1.Isolate the radical using the reverse order of operations. 2.Square both sides (the radical & the squared symbol cancel each other out) 3.Isolate the variable on one side & solve 4.Check your answers for extraneous solutions.

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

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

5) 6) More examples of Radical Equations

Solve. Check for extraneous solutions. 7)

Solve. Check for extraneous solutions. 8)

Steps for Solving Squared ( )² equations 1.Isolate the variable on one side. 2.If it is squared, take the square root (√) of both sides. 3.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

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

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