Essential Question: Describe the procedure for solving a radical equation

 A radical equation is an equation that has a variable in a radicand or a variable with a rational exponent.  radical equation  not a radical equation  To solve a radical equation, isolate the radical on one side of the equation and then raise both sides of the equation to the inverse power.

 Example:  Goal is to get by itself  Subtract 2 from both sides  Inverse of square root?  Square each side  Add 2 to both sides  Divide both sides by 3

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 Example:  Goal is to get by itself  Divide both sides by 2  Inverse of 2 / 3 power?  Take each side to 3 / 2 power Use absolute values only when taking an even root  Make two equations  Add 2 to both sides

 Example: 

 Assignment  Page 394  1 – 12  All problems  Show work

Essential Question: Describe the procedure for solving a radical equation

 Much like with absolute value equations, you’ll have to check for extraneous solutions.  Part 1 – Solving the problem  Get by itself  Subtract 5, both sides  Square both sides  FOIL right side  Subtract x & add 3  Factor  Solve each parenthesis

 Part 2 – Checking for extraneous solutions  Original Problem  Two solutions  The only solution is x = 7 x = 4x = 7 Plug in for all x’s Simplify under radical Simplify radical Combine like terms ExtraneousReal

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 Part 2 – Checking for extraneous solutions  Original Problem  Two solutions  x = 10x = 1 Real SolutionExtraneous Solution The only solution is x = 10

 Get the two equations on opposite sides  Raise both sides to eliminate the smallest power   FOIL the left side Get equation = 0  Subtract 3x on both sides Subtract 4 on both sides  Factor the equation  Solve each parenthesis 

 Part 2 – Checking for extraneous solutions  Original Problem  Two solutions  Let’s check x = -1 x = 3 / 4 Plug in for all x’s Simplify parenthesis Calculator is your friend Combine like terms Real Solution

 Part 2 – Checking for extraneous solutions  Original Problem  Two solutions  ¾ is the only real solution x =-1 Plug in for all x’s Simplify parenthesis Extraneous Solution (-1) 0.5 is not a real number

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 Assignment  Page  15 – 29  Odd problems  Show work Note: All problems have at least one real solution. Some will also have one extraneous solution & the book will not give you the extraneous solution, but I want both.