3. A radical equation is an equation that contains a radical. BACK

4. The goal in solving radical equations is the same as the goal in solving most equations. BACK

5. We need to isolate the variable. BACK

6. But there is only one way to move the variable out from under the square root sign. BACK

7. We need to square the radical expression. BACK

8. And, because it is an equation, what we do to one side, BACK

9. And, because it is an equation, what we do to one side, we have to do to the other. BACK

10. Remember, no matter what n is. (Even if n is an expression) BACK

11. So we have: BACK

13. Solve for x: Step 1. Simplify the expression: BACK

14. Solve for x: BACK

15. Solve for x: Step 1. Simplify the expression. Step 2. Isolate the radical. BACK

16. Solve for x: BACK

17. Solve for x: Step 1. Simplify the expression. Step 2. Isolate the radical. Step 3. Square both sides. BACK

18. Solve for x: BACK

19. Solve for x: Step 1. Simplify the expression. Step 2. Isolate the radical. Step 3. Square both sides. Step 4. Solve the equation. BACK

20. Solve for x: BACK

21. Try this one: Dude! You try one. BACK

24. Try this one: Dude! You try one. BACK

26. If you have a square root equaling a negative number there is no solution. No Solutions

27. An Extraneous Solution is a solution that does not satisfy the original equation. -2 is an extraneous answer.

28. Watch Out!! If all answers are extraneous, there is also no solution.

30. Since -11 does not satisfy the original equation, 11 is the only solution. -11 is an extraneous solution.

31. Solving Equations with a radical 1.) a 2 = 64 a = 8, or -8 2.) a 2 = 37 a = 37, or - 37 Solve for a

32. Solving Equations with a radical 3.) a 2 = 0 a = 0 4.) a 2 = -25 No Solution Solve for a

33. Solving Equations with a radical 3x 2 - 48 = 0 3x 2 - 48 + 48 = 0 + 48 3x 2 = 48 3x 2 /3 = 48/3 x 2 = 16 x = 16 x =  4

34. BACK