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# Solving Radical Equations and Inequalities - PowerPoint PPT Presentation

Solving Radical Equations and Inequalities. Section 5.8. Radical Equations. Contains variable within a radical Review: How did you solve To Solve: Isolate the radical Raise both sides to a power that is equal to the index of the radical Simplify and solve

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### Solving Radical Equations and Inequalities

Section 5.8

• Contains variable within a radical
• Review: How did you solve
• To Solve:
• Raise both sides to a power that is equal to the index of the radical
• Simplify and solve
• If there are 2 radicals, set up the equation so only 1 radical is on each side of the equation
Extraneous Solutions
• When raising both sides of an equation to an even power, you have to check your answers because you may get extraneous solutions.
• EX: Solve. Check your solutions.
• 1) 2)
Rational Exponents
• Recall:
• Therefore, when you see expressions raised to rational exponents in an equation, you can solve them using similar methods as you used for solving radical equations.
• Raise both sides of equation to reciprocal power of given exponent
• OR rewrite equation as radical equation and solve like previous problems
• EX: Solve
• 1) 2)
• 3)
• Inequality that contains variable within radical
• Solve by using a graph & table OR algebraically
• Similar to 5.5 notes
• Graph & Table:
• Look for where Y1 = Y2 and ERROR
• Algebra:
• Solve Inequality