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

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