Radical Equations with Extraneous Solutions

• x = 5

• x = 6

• x = -5

• x = -6

Name the extraneous solution(s) for this equation.

• 3

• -3 and -4

• 4

• -4

Solve:

• 1

• 43

• 8

• 55

Solve

• -5

• -4

• 4

• -5, 4

• -6

• 6

• -5

• 5

Challenge: SELECT ALL THAT APPLY -

When solving the following Radical Equations, which equations will have EXTRANEOUS solutions.

Challenge: SELECT ALL THAT APPLY - Consider the following: \sqrt[]{5x+11}-1=x After solving, which solution(s) will be solved EXTRANEOUS.

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.

What are solutions that create an imaginary value, or a negative within a square root?

• Extraneous Solutions

• Negative Solutions

• Irrational Solutions

• Radical Solutions

• { 1 }

• { 1, 9 }

• { 9 }

• No Solution