U 2 S 1 L 3 Radical Equations

U 2 -S 1 -L 3 Radical Equations Essential Question: How do you solve radical equations and identify extraneous solutions?

Main Idea & Vocabulary • A radical equation is an equation that contains a radical with a variable. • We will use our solving skills, inverse operations and the property below in this lesson.

Tips 1) 2) 3) 4) Always get the radical symbol alone Square both sides (inverse of rooting) Do inverse operations Check for extraneous solutions (No negative under the radical or equaling the radical)

Ex 1 -Solving Simple Radical Equations

Ex 2 -Solving Radical Equations by Addition or Subtraction

Ex 3 -Solving Radical Equations by Multiplication or Division

Ex 4 -Solving Radical Equations with Square Roots on Both Sides.

Extraneous Solutions • Extraneous solution: a solution that DOES NOT satisfy the original equation. • Example: • Check all solutions!!!!

Ex 5 -Extraneous Solutions • Squaring both sides of an equation can lead to extraneous solutions.

Things to Think About • How do you solve a radical equation with square roots on both sides? • What type of solutions must we look out for when squaring both sides of a radical equation? • How do we know if our solutions are extraneous?

Summary • Answer the essential question in detailed, complete sentences. • How do you solve radical equations and identify extraneous solutions? • Write 3 -5 study questions in the left column to correspond with the notes.