pg. 122 from student journal complete 1-13 1 algebra ii
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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
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√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.
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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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32Algebra II
33Algebra II
1. 2. 3.
4. 5.
1, 5