1. Solving Radical Equations

2. that contains a radical.
A radical equation
is an equation
that contains a radical.

3. mathematical definitions
Did you ever notice
how much sense
mathematical definitions
usually make?

4. in solving most equations.
The goal in solving
radical equations
is the same as the goal
in solving most equations.

5. We need to isolate
the variable.

6. But there is only one way
to move the variable
out from under the
square root sign.

7. We need to square the
radical expression.

8. And, because it is an
equation,
what we do to one side,

9. we have to do to the other.
And, because it is an
equation,
what we do to one side,
we have to do to the other.

10. And now, we need
to simplify:

11. (Even if n is an expression)
Remember,
no matter what
n is.
(Even if n is an expression)

12. So we have:

13. So we have:
So we have:

14. Solve for x:
Step 1. Simplify the expression:

15. Solve for x:

16. Solve for x: Step 1. Simplify the expression.
Step 2. Isolate the radical.

17. Solve for x:

18. Solve for x: Step 1. Simplify the expression.
Step 2. Isolate the radical.
Step 3. Square both sides.

19. Solve for x:

20. Solve for x: Step 1. Simplify the expression.
Step 2. Isolate the radical.
Step 3. Square both sides.
Step 4. Solve the equation.

21. Solve for x:

22. Try this one:
Solve for x:

23. Solve for x: