11.5 Solving Radical Equations

Algebra 2.0

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) Always get the radical symbol alone2) Square both sides3) Do inverse operations 4) Check for extraneous solutions

Ex 1-Solving Simple Radical Equations

Practice 1

Ex 2-Solving Radical Equations byAddition or Subtraction

Ex 2-Solving Radical Equations byAddition or Subtraction

Practice 2

Ex 3-Solving Radical Equations byMultiplication or Division

Practice 3

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

Practice 4

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

Practice 5

Ex 6-Geometry Application• Draw a picture, if necessary.• Use a formula from 7th grade• Solve with Algebra skills

Practice 6

Review

• 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?