How to Solve a Radical Equation 1.Consider the Problem. 2.Put the radicals on different sides of the equals sign. 3.Square both sides. 4.Move all the terms.

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Presentation transcript:

How to Solve a Radical Equation 1.Consider the Problem. 2.Put the radicals on different sides of the equals sign. 3.Square both sides. 4.Move all the terms that don’t involve radicals to one side. 5.Square both sides again. (If radicals remain). 6.Finish Solving 7.Check your solutions in the original equation. 8.State your conclusion home page of … dusty wilsonhome page of … dusty wilson Math 115 home pageMath 115 home page

Warning – To succeed at solving these problems, you must be able to solve problems on your own. This means: a.) No notes. b.) No calculator. c.) No tutor or friend. To accomplish this, you must be able to perform each step prior to seeing it carried out. So, after you think you understand the process, try another problem. Rather than looking at this example to direct you, look at it to check your progress and understanding. Good luck and enjoy some fun problems home page of … dusty wilsonhome page of … dusty wilson Math 115 home pageMath 115 home page

Step 1: Consider the Problem. Notice that there are two radicals in this equation home page of … dusty wilsonhome page of … dusty wilson Math 115 home pageMath 115 home page

Step 2: Put the radicals on different sides of the equals sign. home page of … dusty wilsonhome page of … dusty wilson Math 115 home pageMath 115 home page

Step 3: Square both sides. Write out all squares involving addition as a product. home page of … dusty wilsonhome page of … dusty wilson Math 115 home pageMath 115 home page

Step 4: Move all the terms that don’t involve radicals to one side. Note: If your original problem only contains one radical, this is your first step. home page of … dusty wilsonhome page of … dusty wilson Math 115 home pageMath 115 home page

Step 5: Square both sides again. (If radicals remain). Write out all squares involving addition as a product. home page of … dusty wilsonhome page of … dusty wilson Math 115 home pageMath 115 home page

Step 6: Finish Solving a.) Move all terms to one side. b.) Solve as you see fit – in this case by factoring. x = 7 or x =  1 home page of … dusty wilsonhome page of … dusty wilson Math 115 home pageMath 115 home page

Step 7: Check your solutions in the original equation. Check True False home page of … dusty wilsonhome page of … dusty wilson Math 115 home pageMath 115 home page

Step 8: State your conclusion The solution to the problem below: is: Note: Do not forget to check your solutions. Radical equations can have extraneous solutions. It is even possible for them to have no solution. home page of … dusty wilsonhome page of … dusty wilson Math 115 home pageMath 115 home page