1. Solving Radical Equations
The Power Rule
Equations Containing One Radical

2. Definitions
A Radical Equation must have at least one radicand containing a variable
The Power Rule:
If we raise two equal quantities to the same power, the results are also two equal quantities
If x = y then xn = yn
Warning: These are NOT equivalent Equations!

3. Why are they not Equivalent?
Start with a simple original equation:
x = 3
Square both sides to get a new equation:
x2 = which simplifies to x2 = 9
The only solution to x = 3 is 3
x2 = 9 has two solutions 3 and -3
Raising both sides of the equation to an equal power is called an irreversible step.
Therefore we need to check our solutions to make sure they are valid.

4. Equations Containing One Radical
To eliminate the radical, raise both sides to the index of the radical

5. Sometimes, You First Need to Isolate the Radical
Get the radical alone before raising to a power

6. Practice – on the board

7. Equations Containing Two Radicals
Make sure radicals are on opposite sides
Sometimes you need to repeat the process

8. Equations Containing Two Radicals
Make sure radicals are on opposite sides
Sometimes you need to repeat the process

9. Practice – on the board

10. What Next?
Homework Worksheet