1. Section P3 Radicals and Rational Exponents

2. Square Roots

4. Examples
Evaluate

5. Simplifying Expressions of the Form

7. The Product Rule for Square Roots

8. A square root is simplified when its radicand has no factors other than 1 that are perfect squares.

9. Examples
Simplify:

10. Examples
Simplify:

11. The Quotient Rule for Square Roots

13. Examples
Simplify:

14. Adding and Subtracting Square Roots

15. Two or more square roots can be combined using the distributive property provided that they have the same radicand. Such radicals are called like radicals.

16. Example
Add or Subtract as indicated:

17. Example
Add or Subtract as indicated:

18. Rationalizing Denominators

19. Rationalizing a denominator involves rewriting a radical expression as an equivalent expression in which the denominator no longer contains any radicals. If the denominator contains the square root of a natural number that is not a perfect square, multiply the numerator and the denominator by the smallest number that produces the square root of a perfect square in the denominator.

20. Let’s take a look two more examples:

22. Examples
Rationalize the denominator:

23. Examples
Rationalize the denominator:

24. Other Kinds of Roots

26. Examples
Simplify:

27. The Product and Quotient Rules for nth Roots

29. Example
Simplify:

30. Example
Simplify:

31. Rational Exponents

34. Example
Simplify:

35. Example
Simplify:
Notice that the index reduces on this last problem.

36. Simplify:
(a)
(b)
(c)
(d)

37. Simplify:
(a)
(b)
(c)
(d)