1. 7.5 Solving Radical Equations

2. What is a Radical Expression? A Radical Expression is an equation that has a variable in a radicand or has a variable with a rational exponent. yes no

3. EXAMPLE – Solving a Radical Equation 2 () 2 Square both sides to get rid of the square root

4. EXAMPLE 2 () 2 NO SOLUTION Since 16 doesn’t plug in as a solution. Let’s Double Check that this works Note: You will get Extraneous Solutions from time to time – always do a quick check

5. Let’s Try Some

7. SOLVING MORE COMPLEX EQUATIONS + because we are taking an even power (square root) of both sides

8. RADICAL EQUATIONS ISOLATE RADICAL / RATIONAL RAISE BOTH SIDES TO RECIPROCAL POWER SOLVE FOR THE VARIABLE

9. SOLVING MORE COMPLEX EQUATIONS Raise each side to the 4 th power. This will get you integer powers – much easier to work with! Factor

10. Let’s Try Some... check for extraneous solutions

12. Can graphing calculators help? 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?