1. Warmup

2. 5-6 Solving Radical Equations
Isolate radical, exponentiate both sides

3. Solving Radical Equations
Step 1
Isolate the radical on one side of the equation
Step 2
Raise each side of the equation to a power equal to the index of the radical to eliminate the radical.
Step 3
Solve the resulting polynomial equation. Check your results.
The process of solving radical equations can give extraneous solutions, which do not satisfy the original problem.

4. Solve the equation.
6. 𝑥− −4=−2

5. Solve the equation. Confirm by using a graphing calculator.
If more than one radical, put on opposite sides. Be careful to do things to SIDES, not parts.
Solve the equation. Confirm by using a graphing calculator.

6. Solve the equation. Confirm by using a graphing calculator.

7. Extraneous Roots It is always important to check the solution to an equation in the original equation, but it is especially important when both sides of an equation are raised to a power. If a solution is an approximation, it is sometimes difficult to determine whether a discrepancy is due to rounding or if it is an incorrect solution. Check exact solutions whenever possible.

8. Solving Radical inequalities:
Step 1
If the index of the root is even, identify the values of the variable for which the radicand is nonnegative.
Step 2
Solve the inequality algebraically.
Step 3
Test values in intervals to check your solution.