1. Solving Radical Equations

2. Essential Question: What is a radical equation and how do I solve it?

3. A radical equation is an equation which contains a radical. The radicand in a radical equation must contain a variable(s). is a radical equation is NOT a radical equation

4. Steps for Solving Radical Equations: 1. Isolate the radical on one side of the equation. 2. If the radical is a square root, square each side of the equation. (If the radical is not a square root, raise each side to a power equal to the root index.) 3. Solve the resulting equation. 4. Check your answer(s) to avoid extraneous roots.

5. You must check your answers. The process of squaring the sides of an equation creates a "derived" equation which may not be equivalent to the original equation. Example: -5 = 5 (-5) 2 = 5 2 25 = 25

6. Consequently, solving this new derived equation may create solutions that never previously existed. These "extra" roots that are not true solutions of the original radical equation are called extraneous roots and are rejected as answers.

7. Example 1: Solve Solution: Check:

8. Example 2: Solve Solution: Check:

9. Example 3: Solve Solution: Check:

10. Example 4: Solve Solution: Check: No solution

11. Example 5: Solve: Solution: Check:

12. Example 6: Solve Solution: Check:

13. Example 7: Application The distance d (in nautical miles) that a person can see to the horizon is given by the formula where h is the person’s eye level in feet. a.If a person’s eye level is 16 feet, how many nautical miles can the person see to the horizon?

14. b.A person can see 5.85 nautical miles to the horizon. What is the person’s eye level?

15. Try these : Example 8: Solve Solution: Check:

16. Example 9: Solve: Solution: Check:

17. Example 10: For a fire hose with a nozzle that has a diameter of 2 inches, the flow rate f (in gallons per minute) can be modeled by where p is the nozzle pressure in pounds per square inch. a.If the nozzle pressure is 9 pounds per square inch, what is the flow rate in gallons per minute?

18. b. If the flow rate is 720 gallons per minute, what is the nozzle pressure?

19. Example 11: Solve: Solution: Check: