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Published byDella Welch Modified over 5 years ago

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Ch 10.3 Solving Radical Equations Objective: To solve equations involving square roots (and equations involving perfect squares).

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

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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.

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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!

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

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5) 6) More examples of Radical Equations

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Solve. Check for extraneous solutions. 7)

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Solve. Check for extraneous solutions. 8)

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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

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

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