Algebra 2 7.6 Notes - 7.6 Solving Radical Equations Goals p...

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Solving Radical Equations Goals p Solve equations that contain radicals. p Use radical equations to solve real-life problems. 7.6 VOCABULARY Extraneous solution A solution of a transformed equation that is not a valid solution of the original equation Your Notes Solve 3 x 4 3. 3 x 4 3 Write original equation. 3 x 1 Isolate radical. ( 3 x ) 3 1 3 Cube each side. x 1 Simplify. The solution is 1 . Check this in the original equation. Example 1 Solving a Simple Radical Equation Solve x 2/3 49. x 2/3 49 Write original equation. x 2/3 49 Isolate radical. ( x 2/3 ) 3/2 49 3/2 Raise each side to 3 2 power. x (49 1/2 ) 3 Apply properties of roots. x 7 3 343 Simplify. The solution is 343 . Check this in the original equation. Example 2 Solving an Equation with Rational Exponents 168 Algebra 2 Notetaking Guide Chapter 7
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Your Notes Solve 3 x 4 1 7. Solution 3 x 4 1 7 Write original equation. 3 x 4 8 Isolate radical. ( 3 x 4) 2 8 2 Square each side.
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