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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

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