1. Solving Radical Equations and Inequalities
Algebra II
January 24 & 25

2. Evaluate the following expressions.
Warm - Up
Evaluate the following expressions. 1. 2.
Solution: 16
Solution: - 8

3. Radicals/Exponents
What does it mean when you have a fractions as an exponent? Such as:
What this stands for is: the number in the numerator is the power, and the number in the denominator is the radical power.
So I could write this in another way like:

4. Write each statement in a different form than given. 1. 2. 3.

5. What about negative exponents
What about negative exponents? Remember negative exponent means your doing the inverse.

6. Write each statement in a different form than given. 1. 2. 3.

7. Solve the following rational exponential equation:
Rational Exponents
Solve the following rational exponential equation:
OPTION #1
Step 1: Convert from exponent to radical form:
Step 2: eliminate the radical:
Step 3: Simplify:

8. Solve the following rational exponential equation:
Rational Exponents
Solve the following rational exponential equation:
OPTION #2
Step 1: Raise to the reciprocal power of the original power:
Step 2: Simplify:

9. Solving Radical Equations
A radical equation is an equation with one or more radicals that have variables in their radicand.
Solving Radical Equations Steps
Step 1 Isolate the radical on one side of the equation if necessary.
Step 2 Raise each side of the equation to the same power to get rid of the radical.
Step 3 Solve the equation and check your solution.

10. Solve a radical Equation
Write original equation.
Cube each side.
Simplify.
Subtract 7 from each side.
x = 10
Divide each side by 2.
Solution x = 10
Check.

11. Try These… 1. SOLUTION: x = 512 2. SOLUTION: x = -9 3.

12. Rational Exponent Example
What is the solution of the equation
Write original equation.
Divide each side by 3.
Raise each side to the power of 3/2.
x = 64
Simplify.
Solution x = 64
Check.

13. Solve an equation with a rational Exponent.
Write original equation.
Add 1 to each side.
Raise each side to the power of 4/3.
Apply exponent properties.
x = 14
Solve the equation.
Solution x = 14
Check.

14. Try These… 1. 2. 3.
SOLUTION: x = 25
SOLUTION: x = 1
SOLUTION: x = 6

15. Solve an equation w/ an extraneous solution
Write original equation.
Square each side.
FOIL the left side and simplify the right.
Write in standard form.
Factor.
x = 7 or x = -2
Solve.
x = 7 (The -2 is extraneous)
Check.

16. Solve an equation with 2 radicals
METHOD 1
Write original equation.
Square each side.
FOIL the left side and simplify the right.
Isolate the radical.
Divide both sides by 2 .
Square each side again.
Simplify.
Write in standard form and factor.
x = 2 or x = -1
Solve.
x = -1 (The 2 is extraneous)
Check.

17. Solve an equation with 2 radicals
METHOD 2
Write original equation.
Graph y1 =
Graph y2 =
Find the point of intersection!
You will find that the ONLY point of intersection is (-1, 2). Therefore, -1 is the only solution of the equation.

18. Try These… Solve the equation. Check for extraneous solutions.1. 2. 3.
SOLUTION: x = 1
SOLUTION: x = 0, 4
SOLUTION: x = 3

19. Solve radical inequalities
Use a graph to solve
SOLUTION
Step 1
ENTER the function and y = 3 into the graphing calculator.
Step 2
GRAPH the functions from Step 1.
Step 3
Identify the x-values for which the graph of lies above the graph of y = 3.
SOLUTION: x > 14

20. Solve the following radical inequalities (try by hand)1. 2.
SOLUTION: x > 32
SOLUTION: x ≥ 16

21. Class Work
p. 447 #3-23 odd
p. 456 #5, 7, 13, 17, 23, 27, 37, 45