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**Solving Radical Equations**

11.3 Solving Radical Equations

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**11.3 – Solving Radical Equations**

Goals / “I can…” Solve equations containing radicals Identify extraneous solutions

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**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!

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**11.3 – Solving Radical Equations**

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

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**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 ____________

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**11.3 – Solving Radical Equations**

A radical equation is an equation with a radical in it.

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**11.3 – Solving Radical Equations**

Try

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**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!!!!

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**11.3 – Solving Radical Equations**

If there are square roots on both sides, square both sides to get rid of them.

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**11.3 – Solving Radical Equations**

#1 Solve Standard Form

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**11.3 – Solving Radical Equations**

Check

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**11.3 – Solving Radical Equations**

#2 Solution Standard Form

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**11.3 – Solving Radical Equations**

Check

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**11.3 – Solving Radical Equations**

An extraneous solution is a solution that does not make the original problem true.

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**11.3 – Solving Radical Equations**

Example:

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**11.3 – Solving Radical Equations**

Sometimes an equation has no solution. You can only know this by putting the solution into the original equation.

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**11.3 – Solving Radical Equations**

Solve: x = x + 6

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**11.3 – Solving Radical Equations**

Solve 2x + 6 = 4

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