1. Entry Task You are a passenger in a car. You are using a cell phone that connects with the tower shown. The tower has an effective range of 6 miles. If you look out the window you see the tower and estimate that it is 3 miles from you. How many miles do you have to finish your call? 5.19 miles 3 miles 6 miles

2. 6.5 Solving Square Root and Other Radical Equations Learning Target: I can solve square root and other radical equations

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

4. The goal in solving radical equations is the same as the goal in solving most equations. We need to isolate the variable.

5. Use the following steps when solving an equation with radicals. Step 1Isolate a radical. Arrange the terms so that a radical is isolated on one side of the equation. Solving a Radical Equation. Step 6Check all proposed solutions in the original equation. Step 5Solve the equation. Find all proposed solutions. Step 4Repeat Steps 1-3 if there is still a term with a radical. Step 3Combine like terms. Step 2Square both sides.

6. We need to square the radical expression.

7. What we do to one side, we have to do to the other

8. Now we need to simplify:

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

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

12. Solve for x:

13. Try this one: Check for extraneous solutions

14. EXAMPLE 1 Solve. Solution: Using the Squaring Property of Equality

15. Solve. EXAMPLE 2 Using the Squaring Property with a Radical on Each Side Solution:

16. EXAMPLE 3 Solve Solution: Using the Squaring Property when One Side Has Two Terms After we check our work the solution set is {4}. or

17. EXAMPLE 2 () 2 NO SOLUTION Since 16 doesn’t plug in as a solution. Let’s Double Check that this works Note: You will get Extraneous Solutions from time to time – always do a quick check

18. Solve

20. Can graphing calculators help? SURE! 1.Input for Y1 2.Input x-2 for Y2 3.Graph 4.Find the points of intersection One Solution at (4, 2) To see if this is extraneous or not, plug the x value back into the equation. Does it work?

21. Assignment pg 395 #9-39 odds