Algebra 2 Notes



Algebra 2 Notes Name: ________________

Section 6.7 – Solving Radical Equations & Inequalities

A ____________________ equation contains a ____________________ within a radical. Recall that you can solve quadratic equations by taking the square root of both sides. Similarly, radical equations can be solved by raising both sides to a ____________________.

|Solving Radical Equations |

|Steps |Example |

|1. Isolate the radical. |[pic] |

|2. Raise both sides of the equation to the power equal to the index of the |[pic] |

|radical. | |

|3. Simplify and solve. |[pic] |

|4. Check your answer for extraneous solutions. |[pic] |

Raising each side of an equation to an even power may introduce extraneous solutions, so you need to check your answer(s) by substituting it back into the original equation.

Example 1: Solve each equation.

|a. [pic] |b. [pic] |c. [pic] |

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|d. [pic] |e. [pic] |f. [pic] |

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You can use similar methods to solve equations containing rational exponents. You raise both sides of the equation to the ____________________ of the exponent. You can also rewrite any expressions with rational exponents in radical form and solve as you would other radical equations.

Example 2: Solve each equation.

|a. [pic] |b. [pic] |c. [pic] |

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A radical ____________________ is an inequality that contains a variable within a radical. You can solve radical inequalities by using algebra. Just remember, when you multiply or divide both sides of an inequality by a negative, you need to ____________________ the inequality sign.

Example 3: Solve each inequality.

|a. [pic] |b. [pic] |c. [pic] |

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