Radical Equations with Extraneous Solutions

What is the first step of Radical Equations?

• Check for extraneous solutions.

• Raise each side of the equation to the power of the index.

• Isolate the radical on one side of equations.

• Solve the remaining equation.

what is the second step of Radical Equations

• Solve the remaining equation

• Raise each side of the equation to the power if the index

• Check for extraneous solutions

• Isolate the radical on one side of equations

What is the third step of Radical Equations

• Check for extraneous solutions

• raise each side of the equation to the power of the index

• Solve the remaining equation

• Isolate the radical on one side of the equation

what is the fourth step of Radical Equations

• Solve the remaining equation

• Raise each side of the equation to the power of the index

• Isolate the radical on one side of equations

• Check for extraneous solutions

Solve and check your solution.

• 8

• -8

• 0

• no solution

• x = 1

  9 is extraneous

• x = 3

  -2 is extraneous

• x = 9

  1 is extraneous

• x = -2

  3 is extraneous

• x = 7

  -8 is extraneous

• x = -8

  7 is extraneous

• x = 4

  14 is extraneous

• no solution

Choose the STEPS that are NOT involved with solving RADICAL equations.

• Isolate the radical on one side or both sides of the equation.

• Square all problems involving radicals.

• Square root problem? Square BOTH sides to rid the radical.

• Always take the reciprocal of the square root first before solving.

• Check for EXTRANEOUS roots/solutions.

Challenge: SELECT ALL THAT APPLY - When solving the following Radical Equations, which equations will have EXTRANEOUS solutions.