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6.5 Equations Involving Radicals BobsMathClass.Com Copyright © 2010 All Rights Reserved. 4 1. Isolate the radical on the LHS. Solution: +4 2. Square both sides to “cancel out” the square root. 3. Solve the equation. -3 4. Check the solution in the original equation. Check: Your Turn Problem #1

6.5 Equations Involving Radicals BobsMathClass.Com Copyright © 2010 All Rights Reserved. 5 1. Isolate the radical on the LHS. Solution: -6 2. Square both sides to “cancel out” the square root. 3. Solve the equation. 4. Check the solution in the original equation. Actually, once a square root equals a negative number, we can stop there because this is not possible. This procedure of raising both sides to power may give solutions which do no satisfy the original equation. These solutions are called extraneous solutions. Check: This is not true. Therefore, there is no solution.  Your Turn Problem #2

6.5 Equations Involving Radicals BobsMathClass.Com Copyright © 2010 All Rights Reserved. 6 Solution: 1. Square both sides to “cancel out” the square root. 2. Solve the equation. Remember, when we have an x 2, we need to get zero on one side, factor the binomial or trinomial, then set each factor equal to zero and solve. Right? 3. Check the solutions in the original equation. -2x+ 4 Check : Since both of the answers give a true statement, both numbers will be in the solution set. Your Turn Problem #3 Hint: one of the answers will not check. (x=1 is an extraneous solution.)

6.5 Equations Involving Radicals BobsMathClass.Com Copyright © 2010 All Rights Reserved. 7 Solution: 1. We could divide by 2 on both sides to isolate the radical. But then we will have a rational expression on the RHS. That doesn’t sound too good. Let’s go ahead and square both sides. 2. Solve the equation. 3. Check the solutions in the original equation. Check:  Your Turn Problem #4 Hint: one of the answers will not check. (x=1 is an extraneous solution.)

6.5 Equations Involving Radicals BobsMathClass.Com Copyright © 2010 All Rights Reserved. 8 Solution: 1. Cube both sides to “cancel out” the cube root. 2. Solve the equation. 3.Check the solutions in the original equation. Check : Your Turn Problem #5