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!
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