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0.3 bzca5e 0.3 bzca5e Presentation 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: