1. Dear Power point User,
This power point will be best viewed as a slideshow. At the top
of the page click on slideshow, then click from the beginning.

2. Radicals and Rational Exponents
Chapter 10

3. 10 Radicals and Rational Exponents 10.1 Finding Roots
10.3 Simplifying Expressions Containing Square Roots
10.4 Simplifying Expressions Containing Higher Roots
10.5 Adding, Subtracting, and Multiplying Radicals
10.6 Dividing Radicals
Putting it All Together
10.7 Solving Radical Equations
10.8 Complex Numbers

4. 10.7 Solving Radical Equations
In this section, we will learn how to solve radical equations. An equation containing
A variable in the radicand is a radical equation. Some examples are listed below.
Understand the Steps for Solving a Radical Equation
An extraneous solution is a value that satisfies one of the new equations but does
not satisfy the original equation. Extraneous solutions occur frequently when
solving radical equations, so we must check all possible solutions in the original
equation and discard any that are extraneous.

5. Solve an Equation Containing One Square Root
Example 1
Solve.
Solution
Step 1: The radical is on a side by itself:
Step 2: Square both sides to eliminate the square root.
Square both sides.
Step 3 and 4: do not apply because there are no like terms to combine and no
radicals remain.
Step 5: Solve the equation.
Add 8 to each side.
Step 6: Check b = 12 in the original equation.
The solution set is {12}.

6. The first step is to get the radical on a side by itself.
Example 2
Solve.
Solution
The first step is to get the radical on a side by itself.
Subtract 7 from each side.
Square both sides to eliminate radical.
The square root has been eliminated.
Subtract 3 from each side.
Check w = 13 in the original equation.
Because w = 13 is an extraneous solution,
The equation has no real solution.
False

7. Start by getting the radical on a side by itself.
Example 3
Solve.
Solution
Start by getting the radical on a side by itself.
Add 2 to each side.
Square both sides to eliminate the radical.
Simplify; square the binomial.
Subtract 2y; subtract 4..
Factor. or
Set each factor equal to zero. or
Solve.
The solution set is {-2,0}.
Check y =0 and y = -2 in the original equation.

8. Solve an Equation Containing Two Square Roots
Example 4
Solve.
Solution
Begin by getting a radical on a side by itself.
Add to each side.
Square both sides to eliminate the radical.
Distribute 4 into parenthesis.
Solve equation.
Check b = 8 in the original equation.
The solution set is {8}.

9. Example 5 Square and simplify Solution Substitute 6 for a and for b.
Multiply
Combine like terms.

10. Example 6 Solve each equation. Solution Subtract on both sides.
Divide by negative one on both sides.
Square both sides.
Simplify.
Notice the equation still contains a radical. Therefore, repeat
Steps 1-3. Begin by getting radical on a side by itself.
Subtract 1 and c on both sides.
Divide by -2 on both sides and square both sides.
Simplify.
Check is left to the student. The solution set is {16}.

11. 1) Do not square both sides before getting a radical on a side by
Watch out for two common mistakes that students make when solving an equation like the one in Example 5b.
1) Do not square both sides before getting a radical on a side by
itself. This is incorrect:
2) The second time we perform step 2, watch out for this common
error.
On the left we must multiply using FOIL or the formula
and on the right we must remember to
square the 2. Be
Careful

12. Solve an Equation Containing a Cube Root
Example 7
Solve.
Solution
The steps that were used to solve equations containing square roots can be used to eliminate cube roots. Except to eliminate a cube root, we cube both sides of the equation.
Subtract on both sides.
Cube both sides to eliminate the radicals.
Simplify :
Distribute:
Subtract 7a; add 8.
Check a = 9 in the original equation.
The solution set is {9}.