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Unit 6.7 Solving Radical Equations

Solving Radical Equations

Solving radical equations involves isolating the radical on one side of the equation and then eliminating the radical by raising both sides of the equation to the appropriate power.

Steps to Solve Radical Equations

  1. Isolate the Radical: If there is more than one term involving the radical, isolate one of the radicals on one side of the equation.
  2. Eliminate the Radical: Raise both sides of the equation to the power that matches the radical (square both sides if it is a square root, cube both sides if it is a cube root, etc.).
  3. Solve the Resulting Equation: Solve the equation that results from step 2.
  4. Check for Extraneous Solutions: Substitute the solutions back into the original equation to verify that they are valid solutions.

Solving Radical Expressions

Solve [latex]\sqrt{x} + 2 = 5[/latex] for x

Isolate the Radical

[latex]\sqrt{x} = 5 - 2[/latex]

[latex]\sqrt{x} = 3[/latex]

Eliminate the Radical

[latex]\sqrt{x} ^2 = 3^2[/latex]

Solve the Resulting Equation

[latex]\ x = 9[/latex]

 

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