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9.1E: Exercises

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Practice Makes Perfect

Simplify Expressions with Square Roots

In the following exercises, simplify.

Example 9.1E.34

36

Answer

6

Example 9.1E.35

4

Example 9.1E.36

64

Answer

8

Example 9.1E.37

169

Example 9.1E.38

9

Answer

3

Example 9.1E.39

16​​​​​​​

Example 9.1E.40

100

Answer

10​​​​​​​

Example 9.1E.41

144​​​​​​​

Example 9.1E.42

4

Answer

−2​​​​​​​

Example 9.1E.43

100​​​​​​​

Example 9.1E.44

1

Answer

−1​​​​​​​

Example 9.1E.45

121​​​​​​​

Example 9.1E.46

121

Answer

not a real number

Example 9.1E.47

36

Example 9.1E.48

9

Answer

not a real number​​​​​​​

Example 9.1E.49

49​​​​​​​

Example 9.1E.50

9+16

Answer

5​​​​​​​

Example 9.1E.51

25+144​​​​​​​

Example 9.1E.52

9+16

Answer

7​​​​​​​

Example 9.1E.53

25+144

​​​​​​​Estimate Square Roots

In the following exercises, estimate each square root between two consecutive whole numbers.

Example 9.1E.54

70

Answer

8<70<9​​​​​​​

Example 9.1E.55

55​​​​​​​

Example 9.1E.56

200

Answer

14<200<15

Example 9.1E.57

172

​​​​​​​Approximate Square Roots

In the following exercises, approximate each square root and round to two decimal places.

Example 9.1E.58

19

Answer

4.36​​​​​​​

Example 9.1E.59

21​​​​​​​

Example 9.1E.60

53

Answer

7.28​​​​​​​

Example 9.1E.61

47

​​​​​​​Simplify Variable Expressions with Square Roots

In the following exercises, simplify.

Example 9.1E.62

y2

Answer

y​​​​​​​

Example 9.1E.63

b2​​​​​​​

Example 9.1E.64

a14

Answer

a7​​​​​​​

Example 9.1E.65

w24​​​​​​​

Example 9.1E.66

49x2

Answer

7x​​​​​​​

Example 9.1E.67

100y2​​​​​​​

Example 9.1E.68

121m20

Answer

11m10​​​​​​​

Example 9.1E.69

25h44​​​​​​​

Example 9.1E.70

81x36

Answer

9x18​​​​​​​

Example 9.1E.71

144z84​​​​​​​

Example 9.1E.72

81x18

Answer

9x9​​​​​​​

Example 9.1E.73

100m32​​​​​​​

Example 9.1E.74

64a2

Answer

8a​​​​​​​

Example 9.1E.75

25x2

Example 9.1E.76

144x2y2

Answer

12xy

Example 9.1E.77

196a2b2

Example 9.1E.78

169w8y10

Answer

13w4y5

Example 9.1E.79

81p24q6

Example 9.1E.80

9c8d12

Answer

3c4d6

Examlpe 9.1E.81

36r6s20

Everyday Math

Example 9.1E.82

Decorating Denise wants to have a square accent of designer tiles in her new shower. She can afford to buy 625 square centimeters of the designer tiles. How long can a side of the accent be?

Answer

25 centimeters

Example 9.1E.83

Decorating Morris wants to have a square mosaic inlaid in his new patio. His budget allows for 2025 square inch tiles. How long can a side of the mosaic be?​​​​​​​

Writing Exercises

Example 9.1E.84

Why is there no real number equal to 64?

Answer

Answers will vary.

Example 9.1E.85

What is the difference between 92 and 9?

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This table has four columns and five rows. The columns are labeled, “I can…,” “Confidentally,” “With some help,” and “No – I don’t get it!” Under the “I can…,” column are, “simplify expressions with square roots.,” “estimate square roots.,” “approximate square roots.,” and “4) simplify variable expressions with square roots.” All the other rows under the different columns are empty.

ⓑ On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?


This page titled 9.1E: Exercises is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

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