SOLVING RADICAL EQUATIONS

Objective: solve simple radical equations and check for extraneous solutions

How do you undo a square root or a cube root?

VOCABULARY

Radical Symbol

Square Root Ex. 9 = 3 ∙ 3

Cube Root Ex. 8 = 2 ∙ 2 ∙ 2

Fourth Root etc.

RATIONAL (FRACTION) EXPONENTS

RE-WRITE EACH IN RADICAL FORM:

REMEMBER…A square root “undoes” a square

A cube root “undoes” a cube

THEREFORE…A square “undoes” a square root

A cube “undoes” a cube root

HOW TO SOLVE A RADICAL EQUATION

Step 1: Put in radical form if necessary

Step 2: Get radical symbol alone

Step 3: Square or cube both sides

Step 4: Drop the radical symbol

Step 5: Solve

Step 6: Check your answers!! *Might be

extraneous

EX 1) SOLVE FOR X

EX 2) SOLVE FOR X

EX 3) SOLVE FOR X

EX 4) SOLVE FOR X

SOLVE & CHECK SOLUTIONS

x = 17

SOLVE & CHECK SOLUTIONS

x = 6

SOLVE & CHECK SOLUTIONS

x = 64

SOLVE & CHECK SOLUTIONS

x = -1

SOLVE & CHECK SOLUTIONS

x = 59

SOLVE & CHECK SOLUTIONS

x = 727

SOLVE & CHECK SOLUTIONS

x = 1

x = 4

SOLVE & CHECK SOLUTIONS

x = -2 extraneousx = 1

SOLVE & CHECK SOLUTIONS

No Solution