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Mathematics LibreTexts

1.9E: Exercises

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    30466
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    Practice Makes Perfect

    Simplify Expressions with Square Roots

    In the following exercises, simplify.

    659. \(\sqrt{36}\)

    660. \(\sqrt{4}\)

    661. \(\sqrt{64}\)

    662. \(\sqrt{169}\)

    663. \(\sqrt{9}\)

    664. \(\sqrt{16}\)

    665. \(\sqrt{100}\)

    666. \(\sqrt{144}\)

    667. \(\sqrt{−4}\)

    668. \(\sqrt{−100}\)

    669. \(\sqrt{−1}\)

    670. \(\sqrt{−121}\)

    Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers

    In the following exercises, write as the ratio of two integers.

    671.

    ⓐ 5 ⓑ 3.19

    672.

    ⓐ 8 ⓑ 1.61

    673.

    ⓐ −12−12 ⓑ 9.279

    674.

    ⓐ −16−16 ⓑ 4.399

    In the following exercises, list the ⓐ rational numbers, ⓑ irrational numbers

    675.

    0.75,0.223–,1.391740.75,0.223–,1.39174

    676.

    0.36,0.94729…,2.528–0.36,0.94729…,2.528–

    677.

    0.45–,1.919293…,3.590.45–,1.919293…,3.59

    678.

    0.13–,0.42982…,1.8750.13–,0.42982…,1.875

    In the following exercises, identify whether each number is rational or irrational.

    679.

    ⓐ 25‾‾‾√25 ⓑ 30‾‾‾√30

    680.

    ⓐ 44‾‾‾√44 ⓑ 49‾‾‾√49

    681.

    ⓐ 164‾‾‾‾√164 ⓑ 169‾‾‾‾√169

    682.

    ⓐ 225‾‾‾‾√225 ⓑ 216‾‾‾‾√216

    In the following exercises, identify whether each number is a real number or not a real number.

    683.

    ⓐ −81‾‾‾√−81 ⓑ −121‾‾‾‾‾√−121

    684.

    ⓐ −64‾‾‾√−64 ⓑ −9‾‾‾√−9

    685.

    ⓐ −36‾‾‾‾√−36 ⓑ −144‾‾‾‾√−144

    686.

    ⓐ −49‾‾‾‾√−49 ⓑ −144‾‾‾‾√−144

    In the following exercises, list the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers.

    687.

    −8,0,1.95286…,125,36‾‾‾√,9−8,0,1.95286…,125,36,9

    688.

    −9,−349,−9‾√,0.409–,116,7−9,−349,−9,0.409–,116,7

    689.

    −100‾‾‾‾√,−7,−83,−1,0.77,314−100,−7,−83,−1,0.77,314

    690.

    −6,−52,0,0.714285———,215,14‾‾‾√−6,−52,0,0.714285———,215,14

    Locate Fractions on the Number Line

    In the following exercises, locate the numbers on a number line.

    691.

    34,85,10334,85,103

    692.

    14,95,11314,95,113

    693.

    310,72,116,4310,72,116,4

    694.

    710,52,138,3710,52,138,3

    695.

    25,−2525,−25

    696.

    34,−3434,−34

    697.

    34,−34,123,−123,52,−5234,−34,123,−123,52,−52

    698.

    15,−25,134,−134,83,−8315,−25,134,−134,83,−83

    In the following exercises, order each of the pairs of numbers, using < or >.

    699.

    −1___−14−1___−14

    700.

    −1___−13−1___−13

    701.

    −212___−3−212___−3

    702.

    −134___−2−134___−2

    703.

    −512___−712−512___−712

    704.

    −910___−310−910___−310

    705.

    −3___−135−3___−135

    706.

    −4___−236−4___−236

    Locate Decimals on the Number Line In the following exercises, locate the number on the number line.

    707.

    0.8

    708.

    −0.9−0.9

    709.

    −1.6−1.6

    710.

    3.1

    In the following exercises, order each pair of numbers, using < or >.

    711.

    0.37___0.630.37___0.63

    712.

    0.86___0.690.86___0.69

    713.

    0.91___0.9010.91___0.901

    714.

    0.415___0.410.415___0.41

    715.

    −0.5___−0.3−0.5___−0.3

    716.

    −0.1___−0.4−0.1___−0.4

    717.

    −0.62___−0.619−0.62___−0.619

    718.

    −7.31___−7.3−7.31___−7.3

    Everyday Math

    719.

    Field trip All the 5th graders at Lincoln Elementary School will go on a field trip to the science museum. Counting all the children, teachers, and chaperones, there will be 147 people. Each bus holds 44 people.

    ⓐ How many busses will be needed?
    ⓑ Why must the answer be a whole number?
    ⓒ Why shouldn’t you round the answer the usual way, by choosing the whole number closest to the exact answer?

    720.

    Child care Serena wants to open a licensed child care center. Her state requires there be no more than 12 children for each teacher. She would like her child care center to serve 40 children.

    ⓐ How many teachers will be needed?
    ⓑ Why must the answer be a whole number?
    ⓒ Why shouldn’t you round the answer the usual way, by choosing the whole number closest to the exact answer?

    Writing Exercises

    721.

    In your own words, explain the difference between a rational number and an irrational number.

    722.

    Explain how the sets of numbers (counting, whole, integer, rational, irrationals, reals) are related to each other.

    Self Check

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

    This is a table that has five rows and four columns. In the first row, which is a header row, the cells read from left to right “I can…,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can…” reads “simplify expressions with square roots,” “identify integers, rational numbers, irrational numbers and real numbers,” locate fractions on the number line,” and “locate decimals on the number line.” The rest of the cells are blank

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