Warm-up

• Find the domain and range from these 3 equations.

3 1 4y x

2 6 5 2y x

3 7 3 1y x

3 1 4y x

2 6 5 2y x

3 7 3 1y x

1:[ , )

3:[4, )

D

R

5:[ , )

6: ( , 2]

D

R

3: ( , ]

7:[1, )

D

R

Chapter 6

Section 6-6

Radical Equations

Objectives

• I can solve equations containing radicals

• I can solve equations containing rational exponents

• I can determine if a solution is Extraneous

Solving Radical Equations

• Follow the same rules as any equation

• Variable on left

• Numbers on Right

• Check your answers

Undoing The Square Root

• We undo addition with subtraction

• We undo multiplication with division

• How do we undo the square root?

• We square it!!

Undoing Radicals

2)12( x 12 x

33 )23( x

44 )56( x

23 x

56 x

Radical Equations

• When solving radical equations make sure only the radical is on the left when you start the problem. (This is like solving absolute value)

• ALWAYS Check answers. You may get Extraneous Solutions from radicals.

Example 1

1582 x

682 x

22 6)82( x

3682 x282 x

14x

Example 2

613 3 x

313 x333 3)1( x

271 x

28x

Example 3

4 4 1x

4 3x 2 2( 4) ( 3)x

4 9x 5x

No Solution

Example 4

• . 362 xx

22 )3()62( xx

362 xx

36 x

9x

Undoing Rational Exponents

• We undo the square root by Squaring It

• We undo a rational exponent by using the Reciprocal of that exponent

Undoing Rational Exponents

3

2 232 1x

2 1x

5

4 453 4x

3 4x

Solve an equation with a rational exponentEXAMPLE 4

Solve (x + 2)3/4 – 1 = 7.

(x + 2)3/4 – 1 = 7

(x + 2)3/4 = 8

(x + 2)3/4 4/3= 84/3

x + 2 = (23)4/3

x + 2 = 24

x + 2 = 16

Write original equation.

Add 1 to each side.

Simplify.

Apply properties of exponents.

Raise each side to the power .43

Simplify.

x = 14 Subtract 2 from each side.

Homework

• Worksheet 10-5