Example 8-1a

1. Solve Original equation Add 1 to each side to isolate the radical. Square each side to eliminate the radical. Find the squares. Add 2 to each side. Example 8-1a

2. Original equation Replaceywith38. Simplify. Example 8-1b Check Answer: The solution checks. The solution is38.

3. Solve Example 8-1c Answer:67

4. Solve Original equation Square each side. Find the squares. Isolate the radical. Divide each side by –4.

5. Square each side. Evaluate the squares. Original equation Replace x with 16. Simplify. Evaluate the square roots. Example 8-2b Check Answer:The solution does not check, so there is no real solution.

6. Solve . Example 8-2c Answer:no real solution

7. Solve In order to remove the power, or cube root, you must first isolate it and then raise each side of the equation to the third power. Original equation Subtract 5 from each side. Cube each side. Evaluate the cubes. Example 8-3a

8. Subtract 1 from each side. Divide each side by 3. Original equation Replace y with –42. Simplify. The cube root of –125 is –5. Add. Example 8-3b Check Answer:The solution is –42.

9. Solve Example 8-3c Answer:13

10. Solve Since the radicandof a square root must be greater than or equal to zero,first solve to identify the values of x for which the left side of the inequality is defined. Example 8-4a

11. Now solve . Original inequality Isolate the radical. Eliminate the radical. Add 6 to each side. Divide each side by 3. Answer:The solution is Example 8-4b

12. Test some x values to confirm the solution. Let Use three test values:one less than 2, one between 2 and 5, and one greater than 5. Since the inequality is not satisfied. Since the inequality is satisfied. Since is not a real number, the inequality is not satisfied. Only the values in the intervalsatisfy the inequality. Example 8-4c Check

13. Solve Answer: Example 8-4d