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Beginning and Intermediate Algebra

Sherri Messersmith

Chapter 10

Radicals and Rational Exponents - all with Video Answers

Educators


Section 1

Finding Roots

00:50

Problem 1

Decide whether each statement is true or false. If it is false, explain why.
$$
\sqrt{121}=11 \text { and }-11
$$

Ernest Castorena
Ernest Castorena
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00:22

Problem 2

Decide whether each statement is true or false. If it is false, explain why.
$$
\sqrt{81}=9
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
01:29

Problem 3

Decide whether each statement is true or false. If it is false, explain why.
The square root of a negative number is a negative number.

Ernest Castorena
Ernest Castorena
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01:27

Problem 4

Decide whether each statement is true or false. If it is false, explain why.
The square root of a nonnegative number is always positive.

Narayan Hari
Narayan Hari
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00:28

Problem 5

Find all square roots of each number.
$$
49
$$

Ernest Castorena
Ernest Castorena
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00:26

Problem 6

Find all square roots of each number.
$$
144
$$

Ernest Castorena
Ernest Castorena
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00:24

Problem 7

Find all square roots of each number.
$$
1
$$

Ernest Castorena
Ernest Castorena
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00:33

Problem 8

Find all square roots of each number.
$$
400
$$

Ernest Castorena
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00:30

Problem 9

Find all square roots of each number.
$$
900
$$

Ernest Castorena
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00:37

Problem 10

Find all square roots of each number.
$$
2500
$$

Ernest Castorena
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00:35

Problem 11

Find all square roots of each number.
$$
\frac{4}{9}
$$

Ernest Castorena
Ernest Castorena
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00:48

Problem 12

Find all square roots of each number.
$$
\frac{36}{25}
$$

Ernest Castorena
Ernest Castorena
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00:39

Problem 13

Find all square roots of each number.
$$
\frac{1}{81}
$$

Ernest Castorena
Ernest Castorena
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00:35

Problem 14

Find all square roots of each number.
$$
\frac{1}{16}
$$

Ernest Castorena
Ernest Castorena
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01:11

Problem 15

Find all square roots of each number.
$$
0.25
$$

Narayan Hari
Narayan Hari
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01:01

Problem 16

Find all square roots of each number.
$$
0.01
$$

Narayan Hari
Narayan Hari
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00:16

Problem 17

Find each square root, if possible.
$$
\sqrt{49}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:17

Problem 18

Find each square root, if possible.
$$
\sqrt{144}
$$

Ernest Castorena
Ernest Castorena
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00:14

Problem 19

Find each square root, if possible.
$$
\sqrt{1}
$$

Ernest Castorena
Ernest Castorena
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00:24

Problem 20

Find each square root, if possible.
$$
\sqrt{81}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:17

Problem 21

Find each square root, if possible.
$$
\sqrt{169}
$$

Ernest Castorena
Ernest Castorena
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00:18

Problem 22

Find each square root, if possible.
$$
\sqrt{36}
$$

Ernest Castorena
Ernest Castorena
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00:38

Problem 23

Find each square root, if possible.
$$
\sqrt{-4}
$$

Ernest Castorena
Ernest Castorena
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00:48

Problem 24

Find each square root, if possible.
$$
\sqrt{-100}
$$

Ernest Castorena
Ernest Castorena
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00:26

Problem 25

Find each square root, if possible.
$$
\sqrt{\frac{81}{25}}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:25

Problem 26

Find each square root, if possible.
$$
\sqrt{\frac{121}{4}}
$$

Ernest Castorena
Ernest Castorena
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00:17

Problem 27

Find each square root, if possible.
$$
-\sqrt{36}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
01:02

Problem 28

Find each square root, if possible.
$$
-\sqrt{64}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:28

Problem 29

Find each square root, if possible.
$$
-\sqrt{\frac{1}{121}}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:23

Problem 30

Find each square root, if possible.
$$
-\sqrt{\frac{1}{100}}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
01:02

Problem 31

Find each square root, if possible.
$$
\sqrt{0.04}
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:29

Problem 32

Find each square root, if possible.
$$
-\sqrt{0.36}
$$

Narayan Hari
Narayan Hari
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00:41

Problem 33

Approximate each square root to the nearest tenth and plot it on a number line.
$$
\sqrt{11}
$$

Ernest Castorena
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00:41

Problem 34

Approximate each square root to the nearest tenth and plot it on a number line.
$$
\sqrt{2}
$$

Ernest Castorena
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00:42

Problem 35

Approximate each square root to the nearest tenth and plot it on a number line.
$$
\sqrt{46}
$$

Ernest Castorena
Ernest Castorena
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00:44

Problem 36

Approximate each square root to the nearest tenth and plot it on a number line.
$$
\sqrt{22}
$$

Ernest Castorena
Ernest Castorena
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00:44

Problem 37

Approximate each square root to the nearest tenth and plot it on a number line.
$$
\sqrt{17}
$$

Ernest Castorena
Ernest Castorena
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00:38

Problem 38

Approximate each square root to the nearest tenth and plot it on a number line.
$$
\sqrt{69}
$$

Ernest Castorena
Ernest Castorena
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00:35

Problem 39

Approximate each square root to the nearest tenth and plot it on a number line.
$$
\sqrt{5}
$$

Ernest Castorena
Ernest Castorena
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00:52

Problem 40

Approximate each square root to the nearest tenth and plot it on a number line.
$$
\sqrt{35}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:43

Problem 41

Approximate each square root to the nearest tenth and plot it on a number line.
$$
\sqrt{61}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:43

Problem 42

Approximate each square root to the nearest tenth and plot it on a number line.
$$
\sqrt{8}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
02:01

Problem 43

Decide whether each statement is true or false. If it is false, explain why.
The cube root of a negative number is a negative number.

Ernest Castorena
Ernest Castorena
Numerade Educator
02:32

Problem 44

Decide whether each statement is true or false. If it is false, explain why.
The even root of a negative number is a negative number.

Ernest Castorena
Ernest Castorena
Numerade Educator
02:32

Problem 45

Decide whether each statement is true or false. If it is false, explain why.
The even root of a negative number is a negative number.

Ernest Castorena
Ernest Castorena
Numerade Educator
01:02

Problem 46

Decide whether each statement is true or false. If it is false, explain why.
Every nonnegative real number has two real, even roots.

Narayan Hari
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01:01

Problem 47

Decide whether each statement is true or false. If it is false, explain why.
Explain how to find $\sqrt[3]{64}$

Narayan Hari
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01:02

Problem 48

Decide whether each statement is true or false. If it is false, explain why.
Explain how to find $\sqrt[4]{16}$

Narayan Hari
Narayan Hari
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01:28

Problem 49

Decide whether each statement is true or false. If it is false, explain why.
Does $\sqrt[4]{-81}=-3 ?$ Why or why not?

Narayan Hari
Narayan Hari
Numerade Educator
01:04

Problem 50

Decide whether each statement is true or false. If it is false, explain why.
Does $\sqrt[3]{-8}=-2 ?$ Why or why not?

Narayan Hari
Narayan Hari
Numerade Educator
00:22

Problem 51

Find each root, if possible.
$$
\sqrt[3]{8}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:16

Problem 52

Find each root, if possible.
$$
\sqrt[3]{1}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:21

Problem 53

Find each root, if possible.
$$
\sqrt[3]{125}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:44

Problem 54

Find each root, if possible.
$$
\sqrt[3]{27}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:14

Problem 55

Find each root, if possible.
$$
\sqrt[3]{-1}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:21

Problem 56

Find each root, if possible.
$$
\sqrt[3]{-8}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:28

Problem 57

Find each root, if possible.
$$
\sqrt[4]{81}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:40

Problem 58

Find each root, if possible.
$$
\sqrt[4]{16}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:14

Problem 59

Find each root, if possible.
$$
\sqrt[4]{-1}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:24

Problem 60

Find each root, if possible.
$$
\sqrt[4]{-81}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:19

Problem 61

Find each root, if possible.
$$
-\sqrt[4]{16}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:14

Problem 62

Find each root, if possible.
$$
-\sqrt[4]{1}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:44

Problem 63

Find each root, if possible.
$$
\sqrt[5]{-32}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:25

Problem 64

Find each root, if possible.
$$
-\sqrt[6]{64}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:16

Problem 65

Find each root, if possible.
$$
-\sqrt[3]{-27}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:43

Problem 66

Find each root, if possible.
$$
-\sqrt[3]{-1000}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
01:02

Problem 67

Find each root, if possible.
$$
\sqrt[6]{-64}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
01:02

Problem 68

Find each root, if possible.
$$
\sqrt[6]{-64}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:33

Problem 69

Find each root, if possible.
$$
\sqrt[3]{\frac{8}{125}}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:44

Problem 70

Find each root, if possible.
$$
\sqrt[4]{\frac{81}{16}}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:27

Problem 71

Find each root, if possible.
$$
\sqrt{60-11}
$$

Ernest Castorena
Ernest Castorena
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00:34

Problem 72

Find each root, if possible.
$$
\sqrt{100+21}
$$

Ernest Castorena
Ernest Castorena
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00:35

Problem 73

Find each root, if possible.
$$
\sqrt[3]{100+25}
$$

Ernest Castorena
Ernest Castorena
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00:49

Problem 74

Find each root, if possible.
$$
\sqrt[3]{9-36}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:35

Problem 75

Find each root, if possible.
$$
\sqrt{1-9}
$$

Ernest Castorena
Ernest Castorena
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00:43

Problem 76

Find each root, if possible.
$$
\sqrt{25-36}
$$

Ernest Castorena
Ernest Castorena
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00:42

Problem 77

Find each root, if possible.
$$
\sqrt{5^{2}+12^{2}}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
00:40

Problem 78

Find each root, if possible.
$$
\sqrt{3^{2}+4^{2}}
$$

Ernest Castorena
Ernest Castorena
Numerade Educator
02:07

Problem 79

If $n$ is a positive, even integer and we are not certain that $a \geq 0,$ then we must use the absolute value symbol to evaluate $\sqrt[n]{a^{n}}$. That is, $\sqrt[n]{a^{n}}=|a|$. Why must we use the absolute value symbol?

Zain Haider
Zain Haider
Numerade Educator
01:21

Problem 80

If $n$ is a positive, odd integer, then $\sqrt[n]{a^{n}}=a$ for any value of $a$. Why don't we need to use the absolute value symbol?

Zain Haider
Zain Haider
Numerade Educator
01:02

Problem 81

Simplify.
$$
\sqrt{8^{2}}
$$

Narayan Hari
Narayan Hari
Numerade Educator
00:06

Problem 82

Simplify.
$$
\sqrt{5^{2}}
$$

Amy Jiang
Amy Jiang
Numerade Educator
01:10

Problem 83

Simplify.
$$
\sqrt{(-6)^{2}}
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:07

Problem 84

Simplify.
$$
\sqrt{(-11)^{2}}
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:02

Problem 85

Simplify.
$$
\sqrt{y^{2}}
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:03

Problem 86

Simplify.
$$
\sqrt{d^{2}}
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:01

Problem 87

Simplify.
$$
\sqrt{m^{2}}
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:00

Problem 88

Simplify.
$$
\sqrt{t^{2}}
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:12

Problem 89

Simplify.
$$
\sqrt[3]{5^{3}}
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:03

Problem 90

Simplify.
$$
\sqrt[3]{1^{3}}
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:01

Problem 91

Simplify.
$$
\sqrt[3]{(-4)^{3}}
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:01

Problem 92

Simplify.
$$
\sqrt[3]{(-3)^{3}}
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:06

Problem 93

Simplify.
$$
\sqrt[3]{z^{3}}
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:02

Problem 94

Simplify.
$$
\sqrt[5]{t^{5}}
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:15

Problem 95

Simplify.
$$
\sqrt[4]{h^{4}}
$$

Narayan Hari
Narayan Hari
Numerade Educator
01:01

Problem 96

Simplify.
$$
\sqrt[5]{v^{5}}
$$

Narayan Hari
Narayan Hari
Numerade Educator
00:56

Problem 97

Simplify.
$$
\sqrt[9]{p^{9}}
$$

Zain Haider
Zain Haider
Numerade Educator
00:45

Problem 98

Simplify.
$$
\sqrt[6]{m^{6}}
$$

Zain Haider
Zain Haider
Numerade Educator
00:35

Problem 99

Simplify.
$$
\sqrt{(x+7)^{2}}
$$

Zain Haider
Zain Haider
Numerade Educator
00:40

Problem 100

Simplify.
$$
\sqrt{(a-9)^{2}}
$$

Zain Haider
Zain Haider
Numerade Educator
01:55

Problem 101

Simplify.
$$
\sqrt[3]{(2 t-1)^{3}}
$$

Zain Haider
Zain Haider
Numerade Educator
01:36

Problem 102

Simplify.
$$
\sqrt[5]{(6 r+7)^{5}}
$$

Zain Haider
Zain Haider
Numerade Educator
01:47

Problem 103

Simplify.
$$
\sqrt[4]{(3 n+2)^{4}}
$$

Zain Haider
Zain Haider
Numerade Educator
01:24

Problem 104

Simplify.
$$
\sqrt[3]{(x-6)^{3}}
$$

Zain Haider
Zain Haider
Numerade Educator
01:34

Problem 105

Simplify.
$$
\sqrt[7]{(d-8)^{7}}
$$

Zain Haider
Zain Haider
Numerade Educator
01:25

Problem 106

Simplify.
$$
\sqrt[6]{(4 y+3)^{6}}
$$

Zain Haider
Zain Haider
Numerade Educator