1. 6.4 Solving Radical Equations
Objectives:
Review solving square root equations
Solve equations with other roots

2. Concept: 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. Review – Solving a Radical Equation
1. Get the radical alone. 2 2
Square both sides to get rid of the square root. ( )
3. Solve for the variable.

4. Concept: Solving Other Roots
ISOLATE RADICAL / RATIONAL
RAISE BOTH SIDES
TO RECIPROCAL POWER
SOLVE FOR THE VARIABLE

5. 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

6. EXAMPLE Square both sides. 7x + 2 = 9(3x – 2) Simplify.
Solve
Square both sides.
7x + 2 = 9(3x – 2)
Simplify.
7x + 2 = 27x – 18
Distribute.
20 = 20x
Solve for x.
1 = x

7. Let’s Try Some

8. Let’s Try Some

9. Let’s Try Some

10. 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?