1. Warm Up Simplify each expression. Assume all variables are positive. 1. 2. 3. 4.

2. LO: How to solve equations that have radicals and rational exponents.

3. A radical equation contains a variable within a radical. Recall that you can solve quadratic equations by taking the square root of both sides. Similarly, radical equations can be solved by raising both sides to a power.

4. For a square root, the index of the radical is 2. Remember!

5. Solve each equation. Example 1: Solving Equations Containing One Radical Subtract 5. Simplify. Square both sides. Solve for x. Simplify. Check

6. 7 Example 2: Solving Equations Containing One Radical Divide by 7. Simplify. Cube both sides. Solve for x. Simplify. Check Solve each equation. 3 7 7 5x  7 84 7 

7. Solve the equation. Subtract 4. Simplify. Square both sides. Solve for x. Simplify. Check Example 3

8. Cube both sides. Solve for x. Simplify. Check Example 4 Solve the equation.

9. Divide by 6. Square both sides. Solve for x. Simplify. Check Example 5 Solve the equation.

10. Example 6: Solving Equations Containing Two Radicals Square both sides. Solve Simplify. Distribute. Solve for x. 7x + 2 = 9(3x – 2) 7x + 2 = 27x – 18 20 = 20x 1 = x

11. Square both sides. Solve each equation. Simplify. Solve for x. 8x + 6 = 9x 6 = x Example 7 Check

12. Cube both sides. Solve each equation. Simplify. Distribute. x + 6 = 8(x – 1) Example 8 x + 6 = 8x – 8 14 = 7x 2 = x Check 2 Solve for x.

15. Pg. 378 # 11 – 27 odd, 43 – 47 odd.