1. Rational Exponents and Solving Radical Equations

2. Objective 1:
You will be able to simplify expressions involving rational exponents.

3. What is a Rational Exponent

4. Formal Definition of Rational Exponent
The value of the numerator represents the power of the radicand.
The value of the denominator represents the index or root of the expression.

5. Examples

6. Now it’s your turn to practice
I Have, Who Has Activity

7. Objective 2:
You will be able to solve radical and rational equations.

8. 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

9. EXAMPLE – Solving a Radical Equation2 2
Square both sides to get rid of the square root ( )

10. 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

11. Let’s Try Some

12. Let’s Try Some

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

14. 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?