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0.3 bzca5ePresentation Transcript

• Section P3 Radicals and Rational Exponents
• Square Roots
•
• Examples Evaluate
• Simplifying Expressions of the Form
•
• The Product Rule for Square Roots
• A square root is simplified when its radicand has no factors other than 1 that are perfect squares.
• Examples Simplify:
• Examples Simplify:
• The Quotient Rule for Square Roots
•
• Examples Simplify:
• Adding and Subtracting Square Roots
• 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 .
• Example Add or Subtract as indicated:
• Example Add or Subtract as indicated:
• Rationalizing Denominators
• 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.
• Let’s take a look two more examples:
•
• Examples Rationalize the denominator:
• Examples Rationalize the denominator:
• Other Kinds of Roots
•
• Examples Simplify:
• The Product and Quotient Rules for nth Roots
•
• Example Simplify:
• Example Simplify:
• Rational Exponents
•
•
• Example Simplify:
• Example Simplify: Notice that the index reduces on this last problem.
• (a) (b) (c) (d) Simplify:
• (a) (b) (c) (d) Simplify: