Pg. 122 from Student JournalComplete 1-13

1Algebra II

2Algebra II

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Algebra II

nth Roots and Rational Exponents

“x to the nth power” “the nth root of x to the mth”

6Algebra II

exponent

base

index

exponent

radicand

1. √10

2. 3√81

3. 7√92

4. 4√p

7Algebra II

index: 2 radicand: 10

index: 3

index: 7

index: 4

radicand: 81

radicand: 92

radicand: p

*an index of 2 is understood if one is not written

8Algebra II

1. √x =

2. 3√y2 =

3. 8√52 =

4. 4√95 =

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x ½

y 2/3

5 2/8 = 5 1/4

9 5/4

1. 3 2/9 =

2. 4 3/10 =

3. 6 2/3 =

4. x 9/4 =

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9√32

10√43

3√624√x9

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Square Roots 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121,

144…

Cube Roots1, 8, 27, 64, 125, 216, 343, 512, 729,

1000…

Fourth Roots1, 16, 81, 256, 625, 1296…

Fifth Roots1, 32, 243, 1024, 3125…

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1. 3√-125 =

2. 4√16 =

3. 5√-32 =

4. 3√27 =

5. 93/2 =

6. 32 -2/5 =

7. 165/2 =

8. 64-2/3 =

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-5

2

-2

3

1 = 1 = 15√322 22 4

2√165 = 45

2√93 = 33 = 27

1 = 1 = 1 3√642 42 16

Evaluate each without a calculator.

14Algebra II

Evaluate each without a calculator.

15Algebra II

Use a calculator to find each value

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17Algebra II

1. 2x4 = 162

x4 = 81

4√x4 = 4√81

x = ±3

2. (x – 2)3 = 10

3√(x – 2)3 = 3√10

x – 2 = 3√10

x = 2 +

3√10

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Only put a ± when the index is even!

3. 2(y - 1)5 = -64 (y – 1)5 = -32 5√(y – 1)5 = 5√-32 y – 1 = -2 y = 1 – 2 y = -1

4. 2(x + 1)2 = 72 (x + 1)2 = 36 2√(x + 1)2 = 2√36 x + 1 = ± 6 x = -1 ± 6x = -1+6 x = -1-6x = 5 x = -7

19Algebra II

Only put a ± when the index is even!

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21Algebra II

Square Roots 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121,

144…

Cube Roots1, 8, 27, 64, 125, 216, 343, 512, 729,

1000…

Fourth Roots1, 16, 81, 256, 625, 1296…

Fifth Roots1, 32, 243, 1024, 3125…

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1. 3√54

Cube Roots:

1,8,27,64,125,216,3433√54 = 3√27∙2 =3√27∙3√2 =

33√2

2. 4√64

Fourth Roots

1,16,81,256

4√64 =

4√16∙4√4 =

2 4√4

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3. 3√48

Cube Roots:

1,8,27,64,125,216,3433√48 = 3√8∙6 =3√8∙3√6 =

23√6

4. 4√162

Fourth Roots

1,16,81,256

4√162 =

4√81∙4√2 =

3 4√2

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5. 3√250y7

Cube Roots:

1,8,27,64,125,216,343

3√125∙2∙y7

5y2 3√2y

6.

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7. 3√81z5

Cube Roots:

1,8,27,64,125,216,343

3√81z5 =3√27∙3∙z5 =

3z 3√3z2

8. 4√162x9

Fourth Roots

1,16,81,256

4√162x9 =

4√81∙2∙x9 =

3x2 4√2x

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9. 3√56x3z5

Cube Roots:

1,8,27,64,125,216,34

3

3√8·7x3z5 =

2xz 3√7z2

10. 4√48x12y15

Fourth Roots

1,16,81,256

4√48x12y15=

4√16∙3x12y15 =

2x3y3 4√3y3

Algebra II 28

1. The equation to estimate wind chill temperature C, for an air temperature of 5° F and a wind speed of s miles per hour is C = 69.2(0.94s) – 50. What would the windchill temperature be if the wind speed is 20 mph.

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30Algebra II

2. The shot used in men's shot put has a volume of about 905 cubic centimeters. Find the radius of the shot. Round to the nearest hundredth. (Hint: Use the Formula V= 4/3πr3)

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1. 2. 3.

4. 5.

1, 5