1. Solving Radical Equations
11.3
Solving Radical Equations

2. 11.3 – Solving Radical Equations
Goals / “I can…”
Solve equations containing radicals
Identify extraneous solutions

3. 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!

4. 11.3 – Solving Radical Equations
Inverse Operations
So… consider this: How could you solve for x now?
Solve by doing the inverse operation: SQUARING!

5. 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 ____________

6. 11.3 – Solving Radical Equations
A radical equation is an equation with a radical in it.

7. 11.3 – Solving Radical Equations
Try

8. 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!!!!

9. 11.3 – Solving Radical Equations
If there are square roots on both sides, square both sides to get rid of them.

10. 11.3 – Solving Radical Equations
#1 Solve
Standard Form

11. 11.3 – Solving Radical Equations
Check

12. 11.3 – Solving Radical Equations
#2 Solution
Standard Form

13. 11.3 – Solving Radical Equations
Check

14. 11.3 – Solving Radical Equations
An extraneous solution is a solution that does not make the original problem true.

15. 11.3 – Solving Radical Equations
Example:

16. 11.3 – Solving Radical Equations
Sometimes an equation has no solution.
You can only know this by putting the solution into the original equation.

17. 11.3 – Solving Radical Equations
Solve:
x =
x + 6

18. 11.3 – Solving Radical Equations
Solve
2x + 6 = 4