Solving Radical Equations 11.3 Solving Radical Equations

11.3 – Solving Radical Equations Goals / “I can…” Solve equations containing radicals Identify extraneous solutions

11.3 – Solving Radical Equations Inverse Operations How would you solve the following equation? Solve by taking the SQUARE ROOT. Why? Square roots and Squaring are inverse operations… they “undo” eachother!

11.3 – Solving Radical Equations Inverse Operations So… consider this: How could you solve for x now? Solve by doing the inverse operation: SQUARING!

A Refresher on Inverses (opposites): 11.3 – Solving Radical Equations A Refresher on Inverses (opposites): Opposite of Multiply is ____________ Opposite of Add is ____________ Opposite of Divide is ____________ Opposite of Subtract is ____________ Opposite of squaring is ____________ Opposite of square rooting is ____________

11.3 – Solving Radical Equations A radical equation is an equation with a radical in it.

11.3 – Solving Radical Equations Try

11.3 – Solving Radical Equations Steps to Solving Radical Eq.’s Isolate the radicand – get all radicands on one side and all constants on the other. Square both sides of the equation Solve for x CHECK YOUR ANSWER!!!!

11.3 – Solving Radical Equations If there are square roots on both sides, square both sides to get rid of them.

11.3 – Solving Radical Equations #1 Solve Standard Form

11.3 – Solving Radical Equations Check

11.3 – Solving Radical Equations #2 Solution Standard Form

11.3 – Solving Radical Equations Check

11.3 – Solving Radical Equations An extraneous solution is a solution that does not make the original problem true.

11.3 – Solving Radical Equations Example:

11.3 – Solving Radical Equations Sometimes an equation has no solution. You can only know this by putting the solution into the original equation.

11.3 – Solving Radical Equations Solve: x = x + 6

11.3 – Solving Radical Equations Solve 2x + 6 = 4