Understanding Elementary Algebra with Geometry

Problem 1

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{4}$$

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Problem 2

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{9}$$

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Problem 3

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$-\sqrt{4}$$

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Problem 4

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$-\sqrt{9}$$

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Problem 5

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{-4}$$

Amy Jiang

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Problem 6

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{-9}$$

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Problem 7

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{25}$$

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00:12

Problem 8

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{49}$$

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Problem 9

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$-\sqrt{100}$$

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Problem 10

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$-\sqrt{36}$$

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Problem 11

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{64}$$

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Problem 12

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{81}$$

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Problem 13

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{121}$$

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Problem 14

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{144}$$

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Problem 15

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{169}$$

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Problem 16

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{196}$$

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Problem 17

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{225}$$

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Problem 18

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{256}$$

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Problem 19

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{289}$$

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Problem 20

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{324}$$

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Problem 21

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{361}$$

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Problem 22

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{400}$$

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Problem 23

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{3} \sqrt{3}$$

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Problem 24

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{10} \sqrt{10}$$

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Problem 25

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{29} \sqrt{29}$$

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Problem 26

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{67} \sqrt{67}$$

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Problem 27

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$(\sqrt{11})^{2}$$

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Problem 28

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$(\sqrt{5})^{2}$$

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Problem 29

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$(\sqrt{33})^{2}$$

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Problem 30

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$(\sqrt{41})^{2}$$

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Problem 31

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{x} \sqrt{x}$$

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Problem 32

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$(\sqrt{x})^{2}$$

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00:25

Problem 33

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$(\sqrt{7})^{4}$$

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00:27

Problem 34

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$(\sqrt{3})^{6}$$

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00:28

Problem 35

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$(\sqrt{7})^{5}$$

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00:28

Problem 35

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$(\sqrt{7})^{5}$$

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00:34

Problem 36

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$(\sqrt{3})^{7}$$

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00:15

Problem 37

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{25-9}$$

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00:14

Problem 38

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{100}-\sqrt{36}$$

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Problem 39

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{25}-\sqrt{9}$$

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Problem 40

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$\sqrt{100-36}$$

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Problem 41

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$(\sqrt{25}-\sqrt{9})^{2}$$

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Problem 42

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$(\sqrt{100-36})^{2}$$

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Problem 43

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$(\sqrt{25-9})^{2}$$

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00:21

Problem 44

Evaluate or simplify each expression. (Assume $x \geq 0 .)$
$$(\sqrt{100}-\sqrt{36})^{2}$$

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00:24

Problem 45

Use a calculator to find the following square roots. Round off your answers to the nearest hundredth.
$$\sqrt{425}$$

Amy Jiang

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Problem 46

Use a calculator to find the following square roots. Round off your answers to the nearest hundredth.
$$\sqrt{983}$$

Amy Jiang

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Problem 47

Use a calculator to find the following square roots. Round off your answers to the nearest hundredth.
$$\sqrt{637}$$

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Problem 48

Use a calculator to find the following square roots. Round off your answers to the nearest hundredth.
$$\sqrt{730}$$

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Problem 49

Use a calculator to find the following square roots. Round off your answers to the nearest hundredth.
$$\sqrt{73.6}$$

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Problem 50

Use a calculator to find the following square roots. Round off your answers to the nearest hundredth.
$$\sqrt{58.9}$$

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Problem 51

Use a calculator to find the following square roots. Round off your answers to the nearest hundredth.
$$\sqrt{2.09}$$

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Problem 52

Use a calculator to find the following square roots. Round off your answers to the nearest hundredth.
$$\sqrt{7.85}$$

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Problem 53

Use a calculator to find the following square roots. Round off your answers to the nearest hundredth.
$$\sqrt{0.037}$$

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Problem 54

Use a calculator to find the following square roots. Round off your answers to the nearest hundredth.
$$\sqrt{0.00049}$$

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Problem 55

Use a calculator to give decimal approximations rounded to one, two, and three places.
$$\sqrt{17}$$

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00:15

Problem 56

Use a calculator to give decimal approximations rounded to one, two, and three places.
$$\sqrt{23}$$

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00:19

Problem 57

Use a calculator to give decimal approximations rounded to one, two, and three places.
$$\sqrt{110}$$

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Problem 58

Use a calculator to give decimal approximations rounded to one, two, and three places.
$$\sqrt{260}$$

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00:40

Estimate the given square root between two consecutive integers without using a calculator, then use a calculator to find the square root rounded to two decimal places to confirm your estimate.
$$\sqrt{73}$$

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Problem 60

Amy Jiang

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00:38

Problem 61

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Problem 62

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00:27

Problem 63

Amy Jiang

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00:35

Problem 64

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00:26

Problem 65

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00:27

Problem 66

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00:23

Problem 67

Determining whether a number is a perfect square is not as hard as it might at first seem. For instance, suppose we wanted to know whether the number 648 is a perfect square. Do you see why the square root of 648 must be between 20 and $30 ?$ Can you think of an easy way to check whether 648 can possibly be a perfect square? [Hint: Think about the possible final digit a perfect square can have.] Is 648 a perfect square?

Amy Jiang

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00:15

Problem 68

Use the result of Exercise 67 to check whether 841 can possibly be a perfect square. Is it?

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00:30

Problem 69

Discuss the correctness of the following steps:
$$\begin{aligned}
\sqrt{2} & \underline{z} \sqrt{1+1} \\
& \stackrel{?}{=} \sqrt{1}+\sqrt{1} \\
& \stackrel{?}{=} 1+1 \\
& \stackrel{\underline{2}}{=} 2
\end{aligned}$$

Amy Jiang

Numerade Educator