1. 7.5 Solving Radical Equations

2. What is a Radical Expression?
yes
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 Equation2 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.
Note: You will get Extraneous Solutions from time to time – always do a quick check
Let’s Double Check that this works

5. Let’s Try Some

6. 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 4th power. This will get you integer powers – much easier to work with!
Factor

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

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

12. Can graphing calculators help?
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?