Pg. 122 from Student Journal Complete 1-13 1 Algebra II

Pg. 122 from Student JournalComplete 1-13

1Algebra II

2Algebra II

3Algebra II

4Algebra II

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 =

9Algebra II

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 =

10Algebra II

9√32

10√43

3√624√x9

11Algebra 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…

Algebra II 12

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 =

13Algebra II

-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

16Algebra II

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

18Algebra II

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!

20Algebra II

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…

Algebra II 22

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

Algebra II 23

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

Algebra II 24

√Algebra II 25

5. 3√250y7

Cube Roots:

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

3√125∙2∙y7

5y2 3√2y

6.

Algebra II 26

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

Algebra II 27

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.

Algebra II 29

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)

31Algebra II

32Algebra II

33Algebra II

1. 2. 3.

4. 5.

1, 5