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- 1. Solving <br />Radical<br />Equations<br />Module 14 Topic 4<br />
- 2. Table of Contents<br /><ul><li>Slides 3-4: How to Solve Radical Equations
- 3. Slides 5-20: Examples and Practice Problems
- 4. Slides 21-22: TI Instructions</li></ul>Audio/Video and Interactive Sites<br /><ul><li> Slide 23: Video/Interactive</li></li></ul><li>A radical equation is an equation where there is <br />a variable in the radicand.<br />Radicand: Number or expression under the radical symbol.<br />Examples of Radical Equations:<br />NOT Radical Equations:<br />
- 5. How do I solve a radical equation?<br />To solve a radical equation…<br />Isolate the radical to one side of the equation <br />Then raise both sides of the equation to the same power.<br />Simplify<br />Example:<br />Isolate the Radical (subtract 4 from both sides)<br />Raise both Sides to the same power (square both sides) <br />Simplify<br />
- 6. Equations with Rational Exponents <br />Recall: The square and square root are inverses ( cube and cube root are inverses, and so on.)<br />To solve this equation, you must use the inverse and square both sides.<br />Check your answer.<br />
- 7. No Solution<br />Did you check your answers? If so, you seen that in the second problem, q =2 does not work!!!!! Therefore, 2 is an extraneous solution and the solution is “No Solution”<br />
- 8. Did you check your answers? If so, you seen that in the second problem, x= -5 does not work!!!!! Therefore, -5 is an extraneous solution and the solution is x=0. <br />Solution Set { 0 }<br />
- 9. Solution Set { 4 }<br />
- 10.
- 11. Equations in the form = k can be solved by raising<br />each side of the equation to the power since . <br />Remember to check for extraneous solutions.<br />Check:<br />
- 12. Solution Set { ¼ , 1 }<br />
- 13. No Solution<br />The reason is shown below:<br />You can not get a real answer by taking the 4th root of a negative number.<br />
- 14. Find the nth root of a if n = 2 and a = 81. <br />Find the nth root of a if n = 5 and a = -1024. <br />
- 15. If there are two radicals, isolate both radicals by <br />moving one to the other side of the equal sign.<br /> Example:<br />Isolate the radicals<br />Square both sides<br />Simplify<br />Subtract 3x from both sides<br />Add10 to both sides<br />Divide both sides by 2<br />
- 16. I squared both sides, but now I have an x2?!<br />Don’t panic! Continue to solve as a quadratic <br />equation by either using the Quadratic Formula <br />or by Factoring…but <br />you must check for extraneous solutions.<br />When solving radical equations, extra solutions may come up when you raise both <br />sides to an even power. These extra solutions are called extraneous solutions.<br />Recall, to check for extraneous solutions by plugging in the values you <br />found back into the original problem. If the left side does not equal the <br />right side then you have an extraneous solution. <br />
- 17. Extraneous Solution!<br />
- 18. If you have a root other than a square root, <br />simply raise both sides to the same power as the <br />root. <br />So, if you have a cubic root, raise both sides to the third power, for a fourth <br />root, raise both sides to the fourth power, etc.<br />Algebraic Rule for all Radical Equations:<br />
- 19. Isolate the radical<br />Cube both sides<br />Simplify<br />Subtract 3 from both sides<br />
- 20. Check:<br />Check:<br />This solution does not work, therefore “No Solution”<br />
- 21. Check:<br />This solution, -5, does not work, therefore <br />the solution set is { 0 }<br />
- 22. Using the TI to solve<br />Simply graph both sides of the equation. <br />The x-values of the intersection point(s) are your <br />solution(s).<br />
- 23. Why does the TI only show x = 7?<br />Because 3 is an extraneous solution!<br />Solving Algebraically:<br />
- 24. Practice Problems<br />Practice Problems and Answers<br />Examples, Answers, and Videos<br />

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