radicals 2 solving radical equations...09 radicals2 solvingradicalequations notes.notebook 1 january...

09 Radicals2­SolvingRadicalEquations Notes.notebook

1

January 30, 2018

Oct 14­11:29 PM

Radicals 2 ­ Solving Radical Equations

Standard: A­REI.2 Math Practice: Look for and make use of structureGLOs: #3­Complex ThinkerHW: WS#8Learning Target: • How do you solve a radical equation?• How do you know if the solution is extraneous?

09 Radicals2­SolvingRadicalEquations Notes.notebook

2

January 30, 2018

Jan 28­9:33 PM

Warm Up: Solve for x:a) b)

09 Radicals2­SolvingRadicalEquations Notes.notebook

3

January 30, 2018

Jan 28­9:33 PM

In this unit, we will examine how to solve square root equations. These are equations that have x inside a square root

Steps to Solve a Radical Equation:1. Get the square root expression by itself on one side of the equation

2. Square both sides (to cancel out the radical)

3. Solve the remaining equation using previously learned techniques (typically those involving linear or quadratic equations).

4. Check your solution(s)!*

Whenever you square both sides of an equation, you technically get a new (but related) equation. And sometimes, when you do this, you obtain a solution that may work for the “new” equation, but does not work for the original equation. Such answers are

called extraneous solutions .

So ALWAYS check your answers!

09 Radicals2­SolvingRadicalEquations Notes.notebook

4

January 30, 2018

Jan 28­9:58 PM

Example 1: Solve for x:

Check:

09 Radicals2­SolvingRadicalEquations Notes.notebook

5

January 30, 2018

Jan 29­7:31 AM

Practice: Solve for x:

a) b)

09 Radicals2­SolvingRadicalEquations Notes.notebook

6

January 30, 2018

Jan 28­10:05 PM

Practice: Solve for x:

c) d)

09 Radicals2­SolvingRadicalEquations Notes.notebook

7

January 30, 2018

Jan 28­9:58 PM

Example 2: Solve for x:

Check:

Don’t forget, before you can square both sides, isolate the radical to one side!

09 Radicals2­SolvingRadicalEquations Notes.notebook

8

January 30, 2018

Jan 28­10:05 PM

Practice: Solve for x:

e) f)

09 Radicals2­SolvingRadicalEquations Notes.notebook

9

January 30, 2018

Jan 28­9:58 PM

Example 3: Solve for x:

Check:

Some equations have two square roots. In these cases rearrange the equation to get one square root on each side of the equation, then square both sides.

09 Radicals2­SolvingRadicalEquations Notes.notebook

10

January 30, 2018

Jan 28­10:05 PM

Practice: Solve for x:

g) h)

09 Radicals2­SolvingRadicalEquations Notes.notebook

11

January 30, 2018

Jan 28­9:58 PM

Example 4: Solve for x:

Check: and

09 Radicals2­SolvingRadicalEquations Notes.notebook

12

January 30, 2018

Jan 28­10:05 PM

Practice: Solve for x:

i) j)