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Radical Equations. Solve. Pythagorean’s Theorem. 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.

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2. Pythagorean’s Theorem 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. 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. The bottom of the board must befrom the wall.

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

4. Radical • Solve for x: 1.Squareboth sides of the equation. 2. Isolate the variable. 3.Check the solution.

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

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

7. Try … • Solve for x: 1. Square both sides of the equation. 2. Set 3. Factor 4. Check the solutions.

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

9. Make it Real 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?

10. About the Index • Solve for y: 1. Isolate the 2.4th power both sides of the equation. 3.Check the solution.

11. Graphing Calculator SURE! • Input for Y1 • Input x-2 for Y2 • Graph • 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?

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