1.9E: Exercises
- Page ID
- 30098
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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.
ⓑ 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?