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