1. Solve

2.  Both are solutions of the radical equation, but since the distance from the bottom of the board to the wall must be, – 6 is not a solution of the problem. Example : A ten-foot board leans against an 8-foot wall so that the top end of the board is at the top of the wall. How far must the bottom of the board be from the wall? Let x be the distance from the bottom of the board to the wall. The bottom of the board must be from the wall. Pythagorean’s Theorem

3. What is a Radical Equation?  A Radical Equation is Exampl e  A solution to a radical equation is a number which, when substituted for the variable, gives a true equation. Non - Example

4.   Solve for x: Radical 3. Check the solution. 2. Isolate the variable. 1. Square both sides of the equation.

5.   Solve for x: Sometimes 4. Check the solution. 3. Isolate the variable. 2. Square both sides of the equation. 1. Isolate the radical.

6.   Solve for x: Try … 4. Check the solution. 3. Isolate the variable. 2. Square both sides of the equation. 1. Isolate the radical.

7.   Solve for x: Try … 4. Check the solution s. 2. Set 1. Square both sides of the equation. 3. Factor

8.   The solution that didn’t work is called an solution. Why didn’t one of the solutions work?  An extraneous solution is a solution.  You will only find an extraneous solution when you your answer.

9.  Example : The time T (in seconds) taken for a pendulum of length L (in feet) to make one full swing, back and forth, is given by the formula To the nearest hundredth, how long is a pendulum which takes 2 seconds to complete one full swing? Make it Real

10.  About the Index  Solve for y: 3. Check the solution. 2. 4 th power both sides of the equation. 1. Isolate the

11. Graphing Calculator 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?