Objectives: 1.Be able to solve a radical equation. 2.Be able to solve an equation that contains a rational exponent. Critical Vocabulary: Rational Exponents,

Objectives:1. Be able to solve a radical equation.

2. Be able to solve an equation that contains a rational exponent.

Critical Vocabulary:Rational Exponents, Extraneous Solutions

I. Solving Radical Equations

1195 xExample 1:

221195 x

12195 x

1305 x

26x

1195 2/1 x

222/1 1195 x

12195 x

1305 x

26x

I. Solving Radical Equations

Example 2: 8532 x

1332 x

221332 x

16932 x

1662 x

83x

8532 2/1 x

222/1 1332 x

1332 2/1 x

16932 x

1662 x

83x

I. Solving Radical Equations

Example 3: 3723 x

333 372 x

2772 x

202 x

10x

372 3/1 x

333/1 372 x

2772 x

202 x

10x

I. Solving Radical Equations

Example 4: 58124 x

3124 x

444 312 x

8112 x

802 x

40x

5812 4/1 x

312 4/1 x

444/1 312 x

8112 x

802 x

40x

This can never happen, therefore the answer is NO SOLUTION and you found an extraneous solution.

71)2( 4

3

x

II. Solving Rational Exponent Equations

Example 5:

8)2( 4

3

x

3/43/44/3 8)2( x

3 40962 x

3 40962 x

162 x

14x

7124 3 x

824 3 x

44

4 3 82

x

40962 3 x

33 3 40962 x

3 40962 x

3 40962 x

162 x

14x

23

2 5/1 x

II. Solving Rational Exponent Equations

Example 6:

2

32

3

2

2

3 5/1x

35/1 x

555/1 3x

555/1 3x

243x

23

2 5 x

2

32

3

2

2

3 5 x

35 x

555 3x

243x

Page 456 #3-21 odds, 23-31(15 problems)

Objectives:1. Be able to solve a radical equation.

2. Be able to solve an equation that contains a rational exponent.

3. Be able to solve an equation that may contain extraneous solutions.

4. Be able to solve an equation that contains multiple radicals.

Critical Vocabulary:Rational Exponents, Extraneous Solutions

Warm Up: 084 2

3

x 1072 x

084 2

3

x

WARM UP #1

84 2

3

x

Get the variable and its exponent alone

22

3

x Raise each side to the 2/3 power

3

23

2

2

3

2

x

3 4x

Simplify each side

1072 x Isolate the root

172 x Get rid of the root

2892 x Solve for “x”

287x

WARM UP #2

III. Solving Equations with Extraneous Solutions

Isolate the root

Get rid of the root

Solve for “x”

272 xx

272 xx

4472 2 xxx

320 2 xx320 2 xx

)1)(3(0 xx3x 1x Check for extraneous

solutions

Get rid of the root

Solve for “x”

Check for extraneous solutions

xx 24 xxx 21682

016102 xx016102 xx0)2)(8( xx

8x 2x

III. Solving Equations with Extraneous Solutions

IV. Solving Equations with Multiple Radicals

Move the root

Square Both Sides

Isolate the Root

1352 xx

23252 xxx1352 xx

32

3

x

xSquare Both Sides

Solve for “x”

124962 xxx021102 xx0)3)(7( xx

7x 3xCheck for Extraneous

Solutions

34

962

xxx

Page 457 #34-43, 45-52