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Solving Radical Equations and Inequalities. Section 5.8. Radical Equations. Contains variable within a radical Review: How did you solve To Solve: Isolate the radical Raise both sides to a power that is equal to the index of the radical Simplify and solve

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radical equations
Radical Equations
  • Contains variable within a radical
  • Review: How did you solve
  • To Solve:
    • Isolate the radical
    • Raise both sides to a power that is equal to the index of the radical
    • Simplify and solve
    • If there are 2 radicals, set up the equation so only 1 radical is on each side of the equation
extraneous solutions
Extraneous Solutions
  • When raising both sides of an equation to an even power, you have to check your answers because you may get extraneous solutions.
  • EX: Solve. Check your solutions.
  • 1) 2)
rational exponents
Rational Exponents
  • Recall:
  • Therefore, when you see expressions raised to rational exponents in an equation, you can solve them using similar methods as you used for solving radical equations.
    • Raise both sides of equation to reciprocal power of given exponent
    • OR rewrite equation as radical equation and solve like previous problems
  • EX: Solve
  • 1) 2)
  • 3)
radical inequality
Radical Inequality
  • Inequality that contains variable within radical
  • Solve by using a graph & table OR algebraically
  • Similar to 5.5 notes
    • Graph & Table:
      • Look for where Y1 = Y2 and ERROR
    • Algebra:
      • Solve Inequality
      • Consider Radicand
        • If even index, radicand cannot be negative
ex solve
EX: Solve
  • Solve algebraically AND graphically.
  • 1) 2)
application
Application
  • The time t in seconds that it takes a car to travel a quarter mile when starting from a full stop can be estimated by using the formula , where w is the weight of the car in pounds and p is the power delivered by the engine in horsepower. If the quarter-mile time for a 3590 lb car is 13.4 s, how much power does its engine deliver? Round to the nearest horsepower.
homework
Homework
  • Pages 381-383 #27-49, 51, 58, 59, 60, 62-65